How do you find the greatest common factor of 20, 16?

Question

Aurora Arias · Accepted Answer

The greatest common factor of #20# and #16# is: #4#.

When calculating the GCF of two numbers, for instance, we first find the factors of both numbers; of these, there will be some that are both (at least always be a common factor: the number 1). Well, these common factors, the higher is the GCF. The greatest common factor of a set of numbers is the largest of the numbers that divide exactly all the numbers in the set. 1, 2, 4, 8, and 16 are the 16 factors. 1, 2, 4, 5, 10, and 20 are the 20 factors. Factors of 16 and 20 are as follows: 1, 2, 4. Four is the greatest of these. There is a more practical way to determine a set of numbers' GCF: Come on, here's an illustration: We want calculate #GCF {20, 32, 48}# We factorize the numbers first: #20 = 2^2 cdot 5# #32 = 2^5# #48 = 2^4 cdot 3# Now, we take a factor from bases repeated, i.e. we take only a #2#, because the other bases (#3# and #5#) are no common to the three numbers. The #2# with the lowest exponent is #2^2#. The GCF is: #GCF {20, 32, 48} = 2^2 = 4#.

Skylar Adams · Answer

undefined To find the greatest common factor (GCF) of 20 and 16, you can use either prime factorization or the method of listing factors.

Using prime factorization:
20 = 2^2 * 5
16 = 2^4

The common factors are 2^2 = 4. Therefore, the GCF of 20 and 16 is 4.

Using the method of listing factors:
For 20: 1, 2, 4, 5, 10, 20
For 16: 1, 2, 4, 8, 16

The common factor is 4. Therefore, the GCF of 20 and 16 is 4.