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# Greatest common factor explained

Here's a nice explanation of greatest common factor (or greatest common divisor) along with a few practice example exercises. Let's roll. Created by Sal Khan.

## Want to join the conversation?

• What about bigger numbers like 118 and 204 •   For bigger numbers, you definitely want to use the Euclidean algorithm, which is an easier and faster way to find the answer. For example:

gcd( 118, 204 )
= gcd ( 118, 204 - 118 )
= gcd ( 118, 86 )
= gcd ( 118 - 86, 86 )
= gcd ( 32, 86 )
= gcd ( 32, 86 - 32 )
= gcd ( 32, 54 )
= gcd ( 32, 54 - 32 )
= gcd ( 32, 22 )
= gcd ( 10, 22 )
= gcd ( 10, 2 )
= 2

The simplest variant of the Euclidean algorithm is to keep subtracting the smaller number from the bigger number until you find a problem easy enough that you know the answer to it. And the answer to that easier problem is the same as the answer to your harder problem.
• Does 0 have a GCD? • while I understand the problems that Sal uses in this video, I do not understand their relation to the problems in the attached section. The first question I was faced with was "#'s divisible by both 15 and 8 are also divisible by which of the following: 21,55,35,60,33". I'm sure with the right explanation, this is very simple, but this specific video stops short. The GCF or GCD of (15,8) is 1. I understand that, but that's not what was asked. Is this question in the wrong section? •  Ok Sal does not explain is explicitly in the video, but it is related. ok so first you have to understand what the problem is asking. The problem is asking for a number(the choices) that have the same factor. So 15's factors are 1 and 5, 15. And then for 8 the factors are 1, 2, 4, 8. So which of the choices is divisible by 1, 2, 4, , 1, 5, 8, 15.

21: is not divisible by 2,5,4 8...
While 60 is divisible by all of the factors(1, 2, 4, 5, 8, 15)
The key is to understand the questions!
Hope that helps
• I need to know how to do it with bigger number that's what I do in the exercise. • If you have to find the GCD of bigger numbers, the fastest way is factoring and comparing the factors: If one or both numbers are prime, then your job is very fast.
Let's say you have 318 and 492
Start dividing by the lowest possible prime numbers like 2 and 3 and 5
318(2
159(3
53 --prime
so the factors of 318 are `2` `3` `53`
492(2
246(2
123(3
41 -- prime
so the factors are `2` `2` `3` `41`
Line up the factors
`2` `3` `53`
`2` `2` `3` `41`
both have `2` `3`
so the greatest common divisor of 492 and 318 will be `2 times 3` or 6
A shortcut is to refer to a table of factors and primes which will often give you the results of big numbers as
928 = 2⁵∙29
1189 = 29∙41
You can quickly see that the common factor is 29
so the GCD(928,1189) = 29
• ls there any numer that has the factors 1 2 3 4 5 6 7 8 and 9 • Is GCM a concept in math? I don't know if my teacher said that accidentally instead of GCF. • There shouldn't be "GCM" in math because multiples for values can go on and on forever; all you have to do is keep multiplying the numbers you have by common values.
However, there is certainly the concept and use of GCFs. They are the greatest common factor that divides two numbers, and one use is to simplify fractions. There are also "LCMs" (Least common multiples), and when you add or subtract fractions, you can find an LCM for a smaller value (instead of having to multiply everything together and get very large products for your numerator and denominator).

[R]
• I don't get it. What is the difference between GCD and GCF? • I was trying to complete the 'Divisibility' Exercise. I was unable to get the correct answers. This was the video it had me watch to help me, yet it does not apply to the 'Divisibility' Exercises. What should I watch for help with the 'Divisibility' Exercises? • I believe the lowest common multiple of 1, 2, 3, 4, 5, 6, 7, 8 & 9 is 15,120.

Think of it like this: 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 = 362,880
But if a number has 9 or 6 as a factor, it automatically has 3 as a factor as well, because 3 is a factor of 9 and 6; so we can remove 3 from that list. And if it has 8 as a factor, it automatically has 4 and 2 as factors as well, so we can remove 4 and 2 from that list.
• I'm not really shore what is the difference of (GCD) and (GCF)? • There isn't much of a difference. GCF, which stands for "Greatest common factor", is the largest value of the values you have, that multiplied by whole number is able to "step onto both".
For example, the GCF of 27 and 30 is 3, since if you add 3 repeatedly, it will equal 27 after it is added 9 times and equal 30 after adding 3 10 times.
On the other hand, 15 is not a common factor because though 15+15=30, 15 "skips over" 27. 9 is not a common factor because while adding 9 three times will equal 27, 9 will "skip over" 30 (jump from 27 to 36).
GCD stands for "Greatest common denominator". This is used when you are working with fractions and want to simplify them and find a common denominator so you can add and/or subtract them. 