Greatest Common Factor of 64 and 65

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, 65 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 64 and 65 is 1.

GCF(64,65) = 1

GCF of 64 and 65

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

GCF of:
and

Greatest Common Factor of 64 and 65

GCF of 64 and 65 is 1

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 65


5 65
13 13
1

Prime factors of 65 are 5.Prime factorization of 65 in exponential form is:

65 = 51×131

∴ So by taking common prime factors GCF of 64 and 65 is 1

Greatest Common Factor of 64 and 65 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 65

List of positive integer factors of 65 that divides 65 without a remainder.

1,5,13,65

Greatest Common Factor

We found the factors and prime factorization of 64 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 64 and 65 is 1.

Also check out the Least Common Multiple of 64 and 65

Properties of GCF 64 and 65

(i) The GCF of 64 and 65 is associative

GCF of 64 and 65 = GCF of 65 and 64

Related Greatest Common Factor of 64

Related Greatest Common Factor of 65

Frequently Asked Questions on GCF of 64 and 65

1. What is the GCF of 64 and 65?

Answer: GCF of 64 and 65 is 1.

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 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

4. How to Find the GCF of 64 and 65?

Answer:

Greatest Common Factor of 64 and 65 = 1

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 65

65 = 5 x 13

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 64 and 65 is 1