What is the Greatest Common Factor of 752 and 766?

Greatest common factor (GCF) of 752 and 766 is 2.

GCF(752,766) = 2

We will now calculate the prime factors of 752 and 766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 752 and 766.

How to find the GCF of 752 and 766?

We will first find the prime factorization of 752 and 766. After we will calculate the factors of 752 and 766 and find the biggest common factor number .

Step-1: Prime Factorization of 752

Prime factors of 752 are 2, 47. Prime factorization of 752 in exponential form is:

752 = 2⁴ × 47¹

Step-2: Prime Factorization of 766

Prime factors of 766 are 2, 383. Prime factorization of 766 in exponential form is:

766 = 2¹ × 383¹

Step-3: Factors of 752

List of positive integer factors of 752 that divides 752 without a remainder.

1, 2, 4, 8, 16, 47, 94, 188, 376

Step-4: Factors of 766

List of positive integer factors of 766 that divides 752 without a remainder.

1, 2, 383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 752 and 766. The biggest common factor number is the GCF number.
So the greatest common factor 752 and 766 is 2.

Also check out the Least Common Multiple of 752 and 766