Greatest Common Factor of 52 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 52, 65 i.e. 13 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 52 and 65 is 13.

GCF(52,65) = 13

GCF of 52 and 65

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

GCF of:
and

Greatest Common Factor of 52 and 65

GCF of 52 and 65 is 13

Prime Factorization of 52


2 52
2 26
13 13
1

Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:

52 = 22×131

Prime Factorization of 65


5 65
13 13
1

Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:

65 = 51×131

∴ So by taking common prime factors GCF of 52 and 65 is 13

Greatest Common Factor of 52 and 65 by matching factors method

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1,2,4,13,26,52

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 52 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 52 and 65 is 13.

Also check out the Least Common Multiple of 52 and 65

Properties of GCF 52 and 65

(i) The GCF of 52 and 65 is associative

GCF of 52 and 65 = GCF of 65 and 52

Related Greatest Common Factor of 52

Related Greatest Common Factor of 65

Frequently Asked Questions on GCF of 52 and 65

1. What is the GCF of 52 and 65?

Answer: GCF of 52 and 65 is 13.

2. What are the Factors of 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

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 52 and 65?

Answer:

Greatest Common Factor of 52 and 65 = 13

Step 1: Find the prime factorization of 52

52 = 2 x 2 x 13

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 = 13

Step 4: Therefore, the greatest common factor of 52 and 65 is 13