What is the Greatest Common Factor of 748 and 765?

Greatest common factor (GCF) of 748 and 765 is 17.

GCF(748,765) = 17

We will now calculate the prime factors of 748 and 765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 748 and 765.

How to find the GCF of 748 and 765?

We will first find the prime factorization of 748 and 765. After we will calculate the factors of 748 and 765 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 765

Prime factors of 765 are 3, 5, 17. Prime factorization of 765 in exponential form is:

765 = 3² × 5¹ × 17¹

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 765

List of positive integer factors of 765 that divides 748 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 748 and 765. The biggest common factor number is the GCF number.
So the greatest common factor 748 and 765 is 17.

Also check out the Least Common Multiple of 748 and 765