Greatest Common Factor of 749 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 749, 756 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 749 and 756 is 7.

GCF(749,756) = 7

GCF of 749 and 756

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

GCF of:
and

Greatest Common Factor of 749 and 756

GCF of 749 and 756 is 7

Prime Factorization of 749


7 749
107 107
1

Prime factors of 749 are 7,107. Prime factorization of 749 in exponential form is:

749 = 71×1071

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 749 and 756 is 7

Greatest Common Factor of 749 and 756 by matching factors method

Factors of 749

List of positive integer factors of 749 that divides 749 without a remainder.

1,7,107,749

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 749 and 756. The biggest common factor number is the GCF number.
So the greatest common factor 749 and 756 is 7.

Also check out the Least Common Multiple of 749 and 756

Properties of GCF 749 and 756

(i) The GCF of 749 and 756 is associative

GCF of 749 and 756 = GCF of 756 and 749

Related Greatest Common Factor of 749

Related Greatest Common Factor of 756

Frequently Asked Questions on GCF of 749 and 756

1. What is the GCF of 749 and 756?

Answer: GCF of 749 and 756 is 7.

2. What are the Factors of 749?

Answer: Factors of 749 are 1, 7, 107, 749. There are 4 integers that are factors of 749. The greatest factor of 749 is 749.

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 749 and 756?

Answer:

Greatest Common Factor of 749 and 756 = 7

Step 1: Find the prime factorization of 749

749 = 7 x 107

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 = 7

Step 4: Therefore, the greatest common factor of 749 and 756 is 7