Factor trees are useful way of showing numbers that divide into the larger number.
They’re basically a picture with the number at the top and its factors below.
So, if we look at the number 42, a typical factor tree could look like either one of these:
Notice that the second line in both trees are different. These are still factors of 42 but, if you follow it through to the third line, you’ll get to the prime* factors. These are the numbers we are interested in.
Multiplying them together will give you the original number, so 42 = 2 x 3 x 7
The idea is that the prime factors will allow you to calculate:
- the HCF – meaning the Highest Common Factor. Where you have 2 or more numbers, it is the largest number that will divide into both. Really useful for simplifying fractions.
2 / 3 is a bit easier to deal with!
- the LCM – meaning the Lowest Common Multiple. Great for adding and subtracting fractions.
See how to add fractions for more details.
Most GCSE factor tree questions are grade 4 and valued at around 4 marks. Although there are a couple of methods to calculate HCF and LCM.
Watch these and try the quick test
How to work out the HCF – the easy way
How to work out the LCM – the easy way
How to work out the HCF and LCM using factor trees
An alternative method is to use short division. It’s quite useful and can be used with algebraic equations relatively easily 🙂
How to work out the HCF and LCM using short division
LCM Word problem Lars, Rita and Alan
* Prime numbers are numbers that are only divisible by themselves and one. In the factor trees shown 2, 3 and 7 are all prime numbers. Click here for How to work out prime factors of a number for a quick reminder.
Watch on YouTube:
How to work out HCF – the easy way
How to work out LCM the easy way
How to work out the HCF and LCM using factor trees
How to work out the HCF and LCM using short division
this video really helped thank you.
please thank you love your teaching
This video is very helpful. thank you so much…….
He left out 2 in 12
It is a very useful clip. Next time do PRIME FACTORIZATION.
Thanks that helped me a lot. I’m going to have and exam tomorrow
I passed yaay it’s all because of u sir,u r the bestest
what about 2 in 12
Thx u helped alot
Thanks got end year exam tomorrow 15/06/15 year 8
2:41 “Make sure you have all the factors” He missed out 1 as a factor for
12 =^.^+
Other than that thanks! 😀
Thaaaaaaanks!
good!!
Thanks 🙂
This helped me so much! LCM was a blur in my mind until I saw this vid!
Thank you, this really helped me
Thanks, I’ve got maths GCSE tomorrow and needed to go over this. Helped a
lot and made it interesting. (Well as interesting as maths revision can be)
thanks man you really helped me
I found this really helpful
2 things. The person who invented this method is a genius and secondly,
isn’t there a separate technique for calculating the LCM?
ThAnks a lot
Thank you very much because i didn´t now how to do it and know i now and a
got a very good grade in my test THANK YOUUUUUUUU
Sorry but isnt 2 a factor of 12 also?
really helpful. thanks 😀
Man you saved me before a math test thankyou
BRILLIANT!! My lecturer has been trying to explain this to me forever…. I
only just got it now. Thanks!! you’re a rockstar!!
thanks, this really helps, i’m doing end of year exams and this is a really
helpful and easy way!
This helped a lot. There was another video which was good, but i deduce
that this one was just a little better. Do you use prime factors so you
don’t get “interference” trying to manipulate with the correlating factors
that just get the thing messy? Also, how does that trick work where you
find the LCM by multiplying the remaining factors and the result of finding
the HCF?
thnx
I finally got it thank you very much
youre pro in this !!!!!!!……….my teacher explained a long method!!!
Thanks Simon, this was well explained and really helpful for my stat
assignment…cheers 🙂
My last name is Simmons
Thank you so much! This helps heap
Thank you so much, I appreciate the help! 😉
this helped so much!, my maths teacher is crap….
Check out this video on YouTube:
could you help me with the help me with the LCM of the following terms
A=3^4*5^2, B=2^2*3^3*5^2 and C=3^2*5^3*7 I worked it out as
2^2*3^5*5^3*7 but the markscheme does not agree could you please help me
out. ASAP
thanks i can now finish homework HELPED ALOT!!
so helpful cheers
Finally found an easy way. Cheers this’ll help for my maths gcse
thank you so much
Well it’s good but for 12 2 is also a factor
So good
Really helped thanks! Used to be really good at them in Primary school but
didn’t do them for 2-3 years and got rubbish! But im good now! THANKS
Thanks this helped me so much with my mats revision!My maths teacher taught
it me a way which I didn’t understand, and this has really helped 🙂
Thnx i really needed to refresh my memory
a lot with homework better than my mum would explain it
LOL!!! what about 9??? 😀
Thank u so much my maths teacher does not explain it right im in grdb8 and
I onky figured it out now
thanks this helped
when doing fractions ,finding the lcm is and alternative method? iv seen it
done with out lcm so they are different methods, i wanna know which one
would best suit me.
thank you so much you helped me so much
Ty
Thanks it helped me a lot in my homework!
THANKS, you helped me so much 😀
Thank you so much! It makes me feel better now,haha.
hats off 4 u. u made it so easy .
This doesn’t work?? For example I tried doing this with 36 and 84?? And I
got the hcf of 6 when infact the correct answer is 12?
Thank you again:)
This really helped…thank you
thanx now can finish homework
You missed 2 in the factors of 12
thanks this helped me so much
Lovely God blessed you, you are the best un saludo desde Huesca,
Thank you! You explained it way better !!
Thanks really helps when I forget how to do things in math.
Thx I’ll remember that coz in my test today I got it wrong
How does a factor tree work if the number goes into decimals. Could you
please help I would really appreciate it. Thanks
doesnt 2 go into 12???
Cool amazing asome
2 is also a factor of 12:)
Thank you! I’d forgotten all about these from school so helped with
daughters homework
Doesn’t 9 go in to 45? 😛
thank you Mr.Deacon
thank you so much this has helped in a phenomenal way now I could go to
class without being shouted at your a miracle
This ain’t no minecraft. Wtf.
sir can you pls also help us out in solving quadratic equation…it’ll be
really helpful to us..thankz in advance..:)
thank u so much sir..:)
this helped so much thank you
Thanks this really helps I have a test tomorrow and this will really
help
oops a lot
very useful thank you so very much you have helped me alot
Omg, Thanks so much!
Now I finally get it!
On my worksheet there weren’t any diagrams, this helped heaps!
Thank you 2 much
Now I can do any HCF activities
Great video. I homeschool my son. We are doing fractions. This was very
helpful. Thank you.
You left out 2 as a factor for 12
I can not thank you enough for this video !!! It helped me save alot of
time on my GRE. Thanks alot !!!
you have a very punchable face +Simon Deacon
Yay! This helped me study for a big test! I hope I get good marks
f~u~c~k U
ur the best
how is it 2x2x3 dont get it
I was looking for Shotbow HCF!
Thanks!
thanks mate needed to refresh my memory
Thank you so much! very helpful
Thank you so much if you hadn’t helped me I wouldn’t have passed my test!!!
could u plz teach how to work out a velocity time graph
You helped me do my home work thanks 😀
Thank you I wish you were my teacher
thank you so much ,this has helped me a lot with revision
thank you so much this is a lot easier than my maths teachers made it out
to be
thank you sooo much. my memory kinda ran dry, and i forgot how to do this
hi Simon Deacon thank you it helped me at my maths homework 🙂
u are da man……man
thanks
thanks for the info but how do you solve the hcf with three numbers like
3,12 , 24
GREAT GUY, GREAT METHOD!
Why did you only use one set of threes though?? Because there was two
threes left and a two??v
very useful like your videos you should make one on area of circles and
circumference
Thank you sir we appreciate your hard work .
night before exam revision and you really helped out thanks soooo much
what if there was 2 common multiple? are we gonna add them or something? 😮
Thanks so much for this..It’s gonna be helpful for my test tomoz
Thx
why do u have to talk so much at the start?
how can you forget 2?
THANK YOU SIR, I WAS WORRIED ABOUT NOT KNOWING THIS.
Oh my god this is so much better and faster than the method my math teacher
showed me! Thanks a lot Sir. 🙂
Really helpful for test thanks
8 and 12 =24 and 48
3:00
Dude, 2 can go into 12!, you forgot to add two to the list
You are amazing! Thanks so much I asked my friend to help me and she
confused me so much this is clear and easy to understand 100% recommending
to my friends
THNK YOU SOO MUCH- my maths teacher is really bad so i dnt understand wat
she’s saying neither does the class so this vid really helped whilst doing
my homework
Thanks for the method 😀
That was really helpful.
thanks ….give me a solution. how to solve a algebra for class 10.
Thanks! Homework done and dusted
That was very useful because I was struggling with the LCM method for
homework thanks a lot+ Learn your 8 times tables 😀
thanks bro
Finished my maths homework…thanks!!
Thanks
Thanks I had maths homework favourite subject and at the time I was
confused thanks once again
Thank u Mr Simon u really helped
Thank you! I’m in year seven though what should I do if there is two same
numbers in both time tables?
Mr Deacon, this is brilliant
Thank you so much
Your tone and delivery method is great.
Thanks much
Thanks a lot!
on*
do u hav a vid in prime decomposition?
Thanks so much! It’s really easy to understand and you explain better than
my teachers lol ^_^
What button.. Whaaaaaat button!?
thanks!
but i don’t understand why u multiplied 2 2 3 not 2 3 3
Cheers really easy to understand
OMG thanks for helping me! I did not understand anything from my textbook
🙂
Tahnkyou 😀 you helped me a lot 😀 keep up the good work
I am studying highest common factors for GCSEs in school at the moment, and
this video really helped me, so thanks! 🙂
THANK YOU!
HACKS!
thanks great tutor
Thank you. Now I will teach my son a lesson 😉
This is brilliant I tell you, coming from someone who is horrible at math.
Thank you and THANK YOU
Just found your channel, and this makes sense to me 😀 Thank you.
it was very useful…thanks !
thanks a lot 🙂
This is really cool but im trying to divide bigger numbers like 245 and 90
etc. :p
You really suck you left out 2
thx so much, this really helped 🙂
OMG thank you so much ..Literally hate maths and am so bad in maths lol but
yh got exam in November and this has helped me 🙂
Thanks this really helped me I have been watching LOADS of your videos and
love them all, easy, clear and great methods. Don’t worry about your 8
times table, you will learn them soon enough. hehe :-).
your a lifesaver simon..thank you very much ..because of you and my
hardwork i passed my algebra lessons ty very much 🙂
omg!!! my hero 🙂
thx alott you really help me!!
wow!.thats very quick.
been across your channel a couple of times :D, got my final maths exam
today !, its 2AM this has really helped me; wish i started working this
hard earlier 🙁 in school- thank you so much anyways hoping for a C
You are really helping ps im in year 7 ive missed a lot in school so big
thanks for help
Thank you for the video, LCM HCM and Primes have been a struggle all year.
your videos are amazing!
Really silly but does 2 not go into 12 also? Videos are great wish I knew
about them when I started my course. My exam is tomorrow and only found you
yesterday!!!
this video really helped thank you!!!!! 🙂
the sum is not correct
u missed out two…
can you tell me how to do factorising
+Luker Stormrage
I might do really well in my end of year test courtesy of you and your
great video… Thank you very much!!!
Day has been saved
Saved the day mate
u missed a 2 on the factors of 12 its meant to be1,2,3,4,6 and 12
Thanks alot for helping appreciate it
u just made my confiused path easier TTHANKS ALOTTTTTT…….
Thank you very much !! You can help me to do my math homework (:
Thank you so much for excellent video. I forgot this method which i’d
learnt 20 years before in my school days. Today i found this while
searching for HCF method to guide my daughter. Thanks a lot.
Brilliant
for 12 times 9 times 2 u wrote 12*9 = 2 at 3:50 😀
This is not easy
Thanks
Hi
can u just get to the point ? fucking dumb cunt wasting my time
A very well done sr. I have watched similar video in Italian language as
I’m italian and they were not as clear as your.
you missed out 2 though on the 12 line why?
0:54 is the way to go 🙂
save time
Please say it is not so. Not the last lesson nooooo!
This was very helpful. (Thanks for using youtube educational)
9 is a factor of 45
Thank you huge help, I get 3D trig, quadratics and all the “outside the
box” hard stuff but its the simple things I always run back too haha,
thanks again
Joking I seriously did good thanks!!!
Not good got a b in mock exam
Thankyou very much your very helpful it was very easy to understand!
Please like and leave a comment!
Visit https://www.3minutemaths.co.uk for real maths, tips and techniques.
Please like and leave a comment!
Visit https://www.3minutemaths.co.uk for real maths, tips and techniques.
Isn’t it 3 min maths
Thank you I really enjoyed this
2 is A factor of 12
you are awesome in maths but lol forgetting ur 8 times table
thanks it helped me alot thx vry much
Thank you so much! You saved a lot of my time! Amazing! What are the other
methods of finding the LCM and HCF? What are their different pros and cons?
You’re method is very clear and extremely simple to understand even better
than my maths teacher!
i would like to be in your lessons
Please post, pin, tweet, like or subscribe!
Please post, pin, tweet, like or subscribe!
Please post, pin, tweet, like or subscribe!
Please post, pin, tweet, like or subscribe!
Thank you very much!
thank you really helpful
Brilliant – congrats!
Thanx i passed the exam 😀 Thank thank youuuuuuuu
Hi try ‘How to work out HCF and LCM using factor trees’ on the channel – might help? All best S
My maths teach also told me somethibg about that u have to add the numbers. Ex: hfc:12 & 14 i have use the tree methodso i got 12: 6×2,2×3 ;14: 7×2. So rhe LCM is 2x2x3x6x7=504 i just dont really understand that
That’s great and glad it helped 🙂
u made my life so much easier
Hi Billy – that’s great – congratulations!
I love you! I am in year 8 and got an 8a in my test, so happy all thanks to you!
Hi – yes, 7 is the HCF of 21 and 35. All best S
Hi – yes, the factors of 16 are 1,2,4,8 and 16. Rgds S
ooops 🙂
hi thank you soo much u helped me alot and can ask tht hcf of 21 and 35 is 7??? 🙂
Would 16 be 1,2,4,8,16?
you didn’t put 2 for 8&12 question.
Thanks so much!
Very helpful ! Thank you Simon
HI Ivan – yes it will although might get a little complex when you write all the factors at the end. You could also try How to work out HCF and LCM using short division on the channel.
I hope this helps and thanks for the comment.
All best
S
Will it work for 4 numbers?
I like how your attitude to all your viewers are always positive
Thank you quite helpful
Thank you! It Helped me sooo much 🙂 the teacher did not explain it too well and now i understand!!
we learn that in 2nd or 3 class in school =) lol
Hi – best advice is to try to divide by “2 or 3 or 5 or something else.” The numbers aren’t always so neat but with 75 and 120 try
5 first (will give 15 and 24)
then
3 (will give 5 and 8, which will be the bottom numbers)
So HCF is 15 and LCM is 600.
I hope this helps. Rgds S
Hi – yes, The prime factors of 108 are along the left and then the number at the bottom. You might need to convert this (9 is 3 x 3). So 108 as the sum of its prime factors is:
108 = 2 x 2 x 3 x (3 x 3)
The brackets is 9 from the bottom.
I hope this helps and thanks for the comment. All best S
Can you also work out the prime factors using short division (bus stop method) or is it just Hcfs and Lcms?
what if it only goes into it once! e.g Hcf&Lcm of 75 and 120! -_-
Hi – yes it will – but it’s a really hard question!
Hi – Thanks for the comment. You English is much better than my Indonesian! All best S
It really save me!
My teacher make exercise about finding HCF and LCM with factor trees.
Since I always use the quickest way to find HCF and LCM (my teacher in grade 6 teach my class so we will do UN faster), I never try using factor trees again and forget how to count it. You help me a lot!
Thank you 🙂
I’m sorry for my bad english, I’m still learning.
I’m from Indonesia 🙂
Did it works on 14175 and 101871 ?
helped a lot thanks! 🙂 xx
thank you so much! really helped!
Genius it’s so much simpler now lol
Thanks!!!!!!!!!
Good luck!
My Maths exam is tomorrow and hopefully I’ll pass!
this is the exact numbers that i have in my mid year exam
No prob – good luck with your test 🙂
No prob – good luck with your test 🙂
thanks really helped for maths test tomorrow ;D
yes i also thank you alot because this is for sure going to be in my end of year exam
Thanks helped me a lot 🙂
Its very helpful. Thank you sir.
Hi – there’s a few in the playlist on the channel. I’ve posted one as a video response for you to link through from. Hope they help and all best S
Can u make a video on factoring
Thank you! This really helped me understand it for my end of year test in a couple of weeks!
That’s great – glad it helped 🙂
Thanks a lot…. 🙂 very helpful!
oops ! Thanks for letting me know 🙂
Thank u
Ps.in the minute 3.43 u placed an equal sign not a multiplication sign
Hi – thanks for question. Yes, it works with 3 or more numbers. It can also be used with algebraic equations.
Does this work with 3 numbers?
Thanks got a maths test tomorrow / please hope it goes well
This Helped so much easier way then i learnt thanks :D.
omg! This was the exact same numbers and question on my homework!
thank you so much……:)
thumbs up if u have a maths test tomorrow
This is very helpful. Thanks!
Thank you so much
You*
This really helped, thank yoi sir.
really helpful. thank you very much.
Thanks – great observation. I will be reshooting this as the sound is poor quality. Kind Regards S
Thanks but u put an equal sign rather than time sign at the bottom 3:41
great vid..thanks a million….
Damn I wish I saw this before my monday exam :/
Hi – thanks for comment – best of luck!
Great question!
I’ve posted a video that uses short division to work out HCF – you could use this to find p. The method continues until you can’t use any more common factors to divide. Try putting 12 as the divisor, 24 as the first number with ‘p’ as the second.
As you divide through you’ll get 2 underneath the 24. Underneath the p you need a number so that the 2 and this number can’t be divided anymore.
If you use, say, 3 it would mean that p is 36.
A 5 means p is 60.
Hope this helps.
Got A GCSE grade c foundation paper :3 wish me look (: and this vid really helped! Thanks.
@ImokaRo mate, i’ve got the same exam as you OCR unit 1? good luck mate
Thanks for your comment and good luck for Monday!
maths exam on monday and this really helped thanks 😀
So HCF = numbers in common.
LCM = all factors from each number multiplied together?
Thanks for the video mate! 🙂
Great tutorial! Thanks!
great tutorial !
Great vid really helped!
Thank-you 🙂
Great Explanation. I Really loved it. Understood Perfectly.