What is the Greatest Common Factor of 756 and 762?

Greatest common factor (GCF) of 756 and 762 is 6.

GCF(756,762) = 6

We will now calculate the prime factors of 756 and 762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 756 and 762.

How to find the GCF of 756 and 762?

We will first find the prime factorization of 756 and 762. After we will calculate the factors of 756 and 762 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 762

Prime factors of 762 are 2, 3, 127. Prime factorization of 762 in exponential form is:

762 = 2¹ × 3¹ × 127¹

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 762

List of positive integer factors of 762 that divides 756 without a remainder.

1, 2, 3, 6, 127, 254, 381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 756 and 762. The biggest common factor number is the GCF number.
So the greatest common factor 756 and 762 is 6.

Also check out the Least Common Multiple of 756 and 762