Greatest Common Factor of 60 and 75

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, 75 i.e. 15 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 60 and 75 is 15.

GCF(60,75) = 15

GCF of 60 and 75

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

GCF of:
and

Greatest Common Factor of 60 and 75

GCF of 60 and 75 is 15

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 75


3 75
5 25
5 5
1

Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:

75 = 31×52

∴ So by taking common prime factors GCF of 60 and 75 is 15

Greatest Common Factor of 60 and 75 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 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Greatest Common Factor

We found the factors and prime factorization of 60 and 75. The biggest common factor number is the GCF number.
So the greatest common factor 60 and 75 is 15.

Also check out the Least Common Multiple of 60 and 75

Properties of GCF 60 and 75

(i) The GCF of 60 and 75 is associative

GCF of 60 and 75 = GCF of 75 and 60

Related Greatest Common Factor of 60

Related Greatest Common Factor of 75

Frequently Asked Questions on GCF of 60 and 75

1. What is the GCF of 60 and 75?

Answer: GCF of 60 and 75 is 15.

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 75?

Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.

4. How to Find the GCF of 60 and 75?

Answer:

Greatest Common Factor of 60 and 75 = 15

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 75

75 = 3 x 5 x 5

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

GCF = 3 x 5 = 15

Step 4: Therefore, the greatest common factor of 60 and 75 is 15