What is the Greatest Common Factor of 754 and 772?

Greatest common factor (GCF) of 754 and 772 is 2.

GCF(754,772) = 2

We will now calculate the prime factors of 754 and 772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 754 and 772.

How to find the GCF of 754 and 772?

We will first find the prime factorization of 754 and 772. After we will calculate the factors of 754 and 772 and find the biggest common factor number .

Step-1: Prime Factorization of 754

Prime factors of 754 are 2, 13, 29. Prime factorization of 754 in exponential form is:

754 = 2¹ × 13¹ × 29¹

Step-2: Prime Factorization of 772

Prime factors of 772 are 2, 193. Prime factorization of 772 in exponential form is:

772 = 2² × 193¹

Step-3: Factors of 754

List of positive integer factors of 754 that divides 754 without a remainder.

1, 2, 13, 26, 29, 58, 377

Step-4: Factors of 772

List of positive integer factors of 772 that divides 754 without a remainder.

1, 2, 4, 193, 386

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 754 and 772. The biggest common factor number is the GCF number.
So the greatest common factor 754 and 772 is 2.

Also check out the Least Common Multiple of 754 and 772