Greatest Common Factor of 64 and 68

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 64, 68 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 64 and 68 is 4.

GCF(64,68) = 4

GCF of 64 and 68

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

GCF of:
and

Greatest Common Factor of 64 and 68

GCF of 64 and 68 is 4

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

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2.Prime factorization of 68 in exponential form is:

68 = 22×171

∴ So by taking common prime factors GCF of 64 and 68 is 4

Greatest Common Factor of 64 and 68 by matching factors method

Factors of 64

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

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

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

Greatest Common Factor

We found the factors and prime factorization of 64 and 68. The biggest common factor number is the GCF number.
So the greatest common factor 64 and 68 is 4.

Also check out the Least Common Multiple of 64 and 68

Properties of GCF 64 and 68

(i) The GCF of 64 and 68 is associative

GCF of 64 and 68 = GCF of 68 and 64

Related Greatest Common Factor of 64

Related Greatest Common Factor of 68

Frequently Asked Questions on GCF of 64 and 68

1. What is the GCF of 64 and 68?

Answer: GCF of 64 and 68 is 4.

2. 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.

3. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. How to Find the GCF of 64 and 68?

Answer:

Greatest Common Factor of 64 and 68 = 4

Step 1: Find the prime factorization of 64

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

Step 2: Find the prime factorization of 68

68 = 2 x 2 x 17

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 64 and 68 is 4