What is the Greatest Common Factor of 748 and 756?

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

GCF(748,756) = 4

We will now calculate the prime factors of 748 and 756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 748 and 756.

How to find the GCF of 748 and 756?

We will first find the prime factorization of 748 and 756. After we will calculate the factors of 748 and 756 and find the biggest common factor number .

Step-1: Prime Factorization of 748

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

748 = 2² × 11¹ × 17¹

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 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

Step-4: Factors of 756

List of positive integer factors of 756 that divides 748 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 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