What is the Greatest Common Factor of 749 and 756?

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

GCF(749,756) = 7

We will now calculate the prime factors of 749 and 756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 749 and 756.

How to find the GCF of 749 and 756?

We will first find the prime factorization of 749 and 756. After we will calculate the factors of 749 and 756 and find the biggest common factor number .

Step-1: Prime Factorization of 749

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

749 = 7¹ × 107¹

Step-2: Prime Factorization of 756

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

756 = 2² × 3³ × 7¹

Step-3: Factors of 749

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

1, 7, 107

Step-4: Factors of 756

List of positive integer factors of 756 that divides 749 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

Final Step: Biggest Common Factor Number

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