What is the Greatest Common Factor of 756 and 763?

Greatest common factor (GCF) of 756 and 763 is 7.

GCF(756,763) = 7

We will now calculate the prime factors of 756 and 763, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 756 and 763.

How to find the GCF of 756 and 763?

We will first find the prime factorization of 756 and 763. After we will calculate the factors of 756 and 763 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 763

Prime factors of 763 are 7, 109. Prime factorization of 763 in exponential form is:

763 = 7¹ × 109¹

Step-3: 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

Step-4: Factors of 763

List of positive integer factors of 763 that divides 756 without a remainder.

1, 7, 109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 756 and 763. The biggest common factor number is the GCF number.
So the greatest common factor 756 and 763 is 7.

Also check out the Least Common Multiple of 756 and 763