Greatest Common Factor of 756 and 760

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 756, 760 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 756 and 760 is 4.

GCF(756,760) = 4

GCF of 756 and 760

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

GCF of:
and

Greatest Common Factor of 756 and 760

GCF of 756 and 760 is 4

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

Prime Factorization of 760


2 760
2 380
2 190
5 95
19 19
1

Prime factors of 760 are 2,5,19. Prime factorization of 760 in exponential form is:

760 = 23×51×191

∴ So by taking common prime factors GCF of 756 and 760 is 4

Greatest Common Factor of 756 and 760 by matching factors method

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

Factors of 760

List of positive integer factors of 760 that divides 760 without a remainder.

1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760

Greatest Common Factor

We found the factors and prime factorization of 756 and 760. The biggest common factor number is the GCF number.
So the greatest common factor 756 and 760 is 4.

Also check out the Least Common Multiple of 756 and 760

Properties of GCF 756 and 760

(i) The GCF of 756 and 760 is associative

GCF of 756 and 760 = GCF of 760 and 756

Related Greatest Common Factor of 756

Related Greatest Common Factor of 760

Frequently Asked Questions on GCF of 756 and 760

1. What is the GCF of 756 and 760?

Answer: GCF of 756 and 760 is 4.

2. 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.

3. What are the Factors of 760?

Answer: Factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760. There are 16 integers that are factors of 760. The greatest factor of 760 is 760.

4. How to Find the GCF of 756 and 760?

Answer:

Greatest Common Factor of 756 and 760 = 4

Step 1: Find the prime factorization of 756

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

Step 2: Find the prime factorization of 760

760 = 2 x 2 x 2 x 5 x 19

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 756 and 760 is 4