How do you find the GCF?

There are two ways to find the correct answer.

One way is to make a factor tree of each number, and then mulitiply the common prime factors of both factor trees. A prime number is a number with only two factors, which are 1 and the actual number.

******24***************40
*****6 x 4***********10 x 4
.3 x 2 2 x 2******5 x 2 2 x 2

the prime numbers which are found in both factor trees are "2x2x2" = 8

The second method is to list all factors of each number:

24 -- 1,2,3,4,6,8,12,24
40 -- 1,2,4,5,8,10,20,40

then you look at the biggest number that appears in both lists, which is the number 8.

1,2, and 4 also appears in both lists but you want the biggest number or GCF which is the number 8.

First you have to factor each number all the way.
24
2 X 2 X 2 X3
40
2 X 2 X 2 X 5

Then you have to see what they have in common.
2 X 2 X 2

Multiply all that and that is your answer.
2 X 2 X 2 = 8

8

24,40 (prime factorization)

24 = [2] x [2] x [2] x 3
40 = [2] x [2] x [2] x 5
-----------------------
The GCF of 24,40 is
2 x 2 x 2
= 8

factor each number into primes
24 = 2·2·2·3
40 = 2·2·2·5

take the product of factors that are in both numbers: 2·2·2 = 8
GCF(24,40) = 8

http://www.purplemath.com/modules/lcm_gcf.htm

hope it helps

It is not GCF but it is GCD(Greatest Common Divisor)

2 (24) 2 (40)
2 (12) 2 (20)
2 (6) 2 (10)
3 (3) 5 (5)

GCD = 2 x 2 x 2 = 8