Greatest Common Factor of 72 and 74

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, 74 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 72 and 74 is 2.

GCF(72,74) = 2

GCF of 72 and 74

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

GCF of:
and

Greatest Common Factor of 72 and 74

GCF of 72 and 74 is 2

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 74


2 74
37 37
1

Prime factors of 74 are 2,37. Prime factorization of 74 in exponential form is:

74 = 21×371

∴ So by taking common prime factors GCF of 72 and 74 is 2

Greatest Common Factor of 72 and 74 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 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

Greatest Common Factor

We found the factors and prime factorization of 72 and 74. The biggest common factor number is the GCF number.
So the greatest common factor 72 and 74 is 2.

Also check out the Least Common Multiple of 72 and 74

Properties of GCF 72 and 74

(i) The GCF of 72 and 74 is associative

GCF of 72 and 74 = GCF of 74 and 72

Related Greatest Common Factor of 72

Related Greatest Common Factor of 74

Frequently Asked Questions on GCF of 72 and 74

1. What is the GCF of 72 and 74?

Answer: GCF of 72 and 74 is 2.

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 74?

Answer: Factors of 74 are 1, 2, 37, 74. There are 4 integers that are factors of 74. The greatest factor of 74 is 74.

4. How to Find the GCF of 72 and 74?

Answer:

Greatest Common Factor of 72 and 74 = 2

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 74

74 = 2 x 37

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

GCF = 2

Step 4: Therefore, the greatest common factor of 72 and 74 is 2