How do you find the GCF of 4 numbers?

Answer 1

I have answered this type of question for two numbers, so I'll post it here to get the main idea across, and then I'll put an example for four numbers.

First, for calculating the GCF for two numbers only, figure out the prime factorization of both numbers and find the largest subset of each factorization which is in the other.

e.g. 112 and 36:

112 = 2*2*2*2*7

36 = 2*2*3*3

36 has two 2's, 112 has two 2's also (plus more, but we can't use them since 36 only has two of them). We can't use any 7's since 36 doesn't have any. Similarly we cannot use any 3's.

The best we can do is use 2*2 = 4.

Another example with two numbers:

1260 = 2*2*3*3*5*7

1650 = 2*3*5*5*11

Largest subset = 2*3*5 = 30

Example with four numbers (84, 21, 210 and 1155):

84 = 2*2*3*7

21 = 3*7

210 = 2*3*5*7

1155 = 3*5*7*11

Largest subset = 3*7 = 21

Read more: How_do_you_work_out_the_highest_common_factor_of_two_numbers