Greatest Common Factor of 72 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 72, 75 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 72 and 75 is 3.

GCF(72,75) = 3

GCF of 72 and 75

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

GCF of:
and

Greatest Common Factor of 72 and 75

GCF of 72 and 75 is 3

Prime Factorization of 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

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 72 and 75 is 3

Greatest Common Factor of 72 and 75 by matching factors method

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

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 72 and 75. The biggest common factor number is the GCF number.
So the greatest common factor 72 and 75 is 3.

Also check out the Least Common Multiple of 72 and 75

Properties of GCF 72 and 75

(i) The GCF of 72 and 75 is associative

GCF of 72 and 75 = GCF of 75 and 72

Related Greatest Common Factor of 72

Related Greatest Common Factor of 75

Frequently Asked Questions on GCF of 72 and 75

1. What is the GCF of 72 and 75?

Answer: GCF of 72 and 75 is 3.

2. What are the Factors of 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

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 72 and 75?

Answer:

Greatest Common Factor of 72 and 75 = 3

Step 1: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

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

Step 4: Therefore, the greatest common factor of 72 and 75 is 3