Greatest Common Factor of 60 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 60, 65 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 60 and 65 is 5.

GCF(60,65) = 5

GCF of 60 and 65

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

GCF of:
and

Greatest Common Factor of 60 and 65

GCF of 60 and 65 is 5

Prime Factorization of 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2,3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

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 60 and 65 is 5

Greatest Common Factor of 60 and 65 by matching factors method

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

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 60 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 60 and 65 is 5.

Also check out the Least Common Multiple of 60 and 65

Properties of GCF 60 and 65

(i) The GCF of 60 and 65 is associative

GCF of 60 and 65 = GCF of 65 and 60

Related Greatest Common Factor of 60

Related Greatest Common Factor of 65

Frequently Asked Questions on GCF of 60 and 65

1. What is the GCF of 60 and 65?

Answer: GCF of 60 and 65 is 5.

2. What are the Factors of 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

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 60 and 65?

Answer:

Greatest Common Factor of 60 and 65 = 5

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

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 = 5

Step 4: Therefore, the greatest common factor of 60 and 65 is 5