Greatest Common Factor of 748 and 756

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 748, 756 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 748 and 756 is 4.

GCF(748,756) = 4

GCF of 748 and 756

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

GCF of:
and

Greatest Common Factor of 748 and 756

GCF of 748 and 756 is 4

Prime Factorization of 748


2 748
2 374
11 187
17 17
1

Prime factors of 748 are 2,11,17. Prime factorization of 748 in exponential form is:

748 = 22×111×171

Prime Factorization of 756


2 756
2 378
3 189
3 63
3 21
7 7
1

Prime factors of 756 are 2,3,7. Prime factorization of 756 in exponential form is:

756 = 22×33×71

∴ So by taking common prime factors GCF of 748 and 756 is 4

Greatest Common Factor of 748 and 756 by matching factors method

Factors of 748

List of positive integer factors of 748 that divides 748 without a remainder.

1,2,4,11,17,22,34,44,68,187,374,748

Factors of 756

List of positive integer factors of 756 that divides 756 without a remainder.

1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756

Greatest Common Factor

We found the factors and prime factorization of 748 and 756. The biggest common factor number is the GCF number.
So the greatest common factor 748 and 756 is 4.

Also check out the Least Common Multiple of 748 and 756

Properties of GCF 748 and 756

(i) The GCF of 748 and 756 is associative

GCF of 748 and 756 = GCF of 756 and 748

Related Greatest Common Factor of 748

Related Greatest Common Factor of 756

Frequently Asked Questions on GCF of 748 and 756

1. What is the GCF of 748 and 756?

Answer: GCF of 748 and 756 is 4.

2. What are the Factors of 748?

Answer: Factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748. There are 12 integers that are factors of 748. The greatest factor of 748 is 748.

3. What are the Factors of 756?

Answer: Factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756. There are 24 integers that are factors of 756. The greatest factor of 756 is 756.

4. How to Find the GCF of 748 and 756?

Answer:

Greatest Common Factor of 748 and 756 = 4

Step 1: Find the prime factorization of 748

748 = 2 x 2 x 11 x 17

Step 2: Find the prime factorization of 756

756 = 2 x 2 x 3 x 3 x 3 x 7

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 748 and 756 is 4