What is the Greatest Common Factor of 742 and 756?

Greatest common factor (GCF) of 742 and 756 is 14.

GCF(742,756) = 14

We will now calculate the prime factors of 742 and 756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 742 and 756.

How to find the GCF of 742 and 756?

We will first find the prime factorization of 742 and 756. After we will calculate the factors of 742 and 756 and find the biggest common factor number .

Step-1: Prime Factorization of 742

Prime factors of 742 are 2, 7, 53. Prime factorization of 742 in exponential form is:

742 = 2¹ × 7¹ × 53¹

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 742

List of positive integer factors of 742 that divides 742 without a remainder.

1, 2, 7, 14, 53, 106, 371

Step-4: Factors of 756

List of positive integer factors of 756 that divides 742 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 742 and 756. The biggest common factor number is the GCF number.
So the greatest common factor 742 and 756 is 14.

Also check out the Least Common Multiple of 742 and 756