Greatest Common Factor of 56 and 64

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 56, 64 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 56 and 64 is 8.

GCF(56,64) = 8

GCF of 56 and 64

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 56 and 64

GCF of 56 and 64 is 8

Prime Factorization of 56


2 56
2 28
2 14
7 7
1

Prime factors of 56 are 2,7. Prime factorization of 56 in exponential form is:

56 = 23×71

Prime Factorization of 64


2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:

64 = 26

∴ So by taking common prime factors GCF of 56 and 64 is 8

Greatest Common Factor of 56 and 64 by matching factors method

Factors of 56

List of positive integer factors of 56 that divides 56 without a remainder.

1,2,4,7,8,14,28,56

Factors of 64

List of positive integer factors of 64 that divides 64 without a remainder.

1,2,4,8,16,32,64

Greatest Common Factor

We found the factors and prime factorization of 56 and 64. The biggest common factor number is the GCF number.
So the greatest common factor 56 and 64 is 8.

Also check out the Least Common Multiple of 56 and 64

Properties of GCF 56 and 64

(i) The GCF of 56 and 64 is associative

GCF of 56 and 64 = GCF of 64 and 56

Related Greatest Common Factor of 56

Related Greatest Common Factor of 64

Frequently Asked Questions on GCF of 56 and 64

1. What is the GCF of 56 and 64?

Answer: GCF of 56 and 64 is 8.

2. What are the Factors of 56?

Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.

3. What are the Factors of 64?

Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.

4. How to Find the GCF of 56 and 64?

Answer:

Greatest Common Factor of 56 and 64 = 8

Step 1: Find the prime factorization of 56

56 = 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 64

64 = 2 x 2 x 2 x 2 x 2 x 2

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 56 and 64 is 8