Greatest Common Factor of 68 and 72

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 68, 72 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 68 and 72 is 4.

GCF(68,72) = 4

GCF of 68 and 72

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

GCF of:
and

Greatest Common Factor of 68 and 72

GCF of 68 and 72 is 4

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

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

∴ So by taking common prime factors GCF of 68 and 72 is 4

Greatest Common Factor of 68 and 72 by matching factors method

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

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

Greatest Common Factor

We found the factors and prime factorization of 68 and 72. The biggest common factor number is the GCF number.
So the greatest common factor 68 and 72 is 4.

Also check out the Least Common Multiple of 68 and 72

Properties of GCF 68 and 72

(i) The GCF of 68 and 72 is associative

GCF of 68 and 72 = GCF of 72 and 68

Related Greatest Common Factor of 68

Related Greatest Common Factor of 72

Frequently Asked Questions on GCF of 68 and 72

1. What is the GCF of 68 and 72?

Answer: GCF of 68 and 72 is 4.

2. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

3. 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.

4. How to Find the GCF of 68 and 72?

Answer:

Greatest Common Factor of 68 and 72 = 4

Step 1: Find the prime factorization of 68

68 = 2 x 2 x 17

Step 2: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 68 and 72 is 4