What is the Greatest Common Factor of 748 and 759?

Greatest common factor (GCF) of 748 and 759 is 11.

GCF(748,759) = 11

We will now calculate the prime factors of 748 and 759, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 748 and 759.

How to find the GCF of 748 and 759?

We will first find the prime factorization of 748 and 759. After we will calculate the factors of 748 and 759 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 759

Prime factors of 759 are 3, 11, 23. Prime factorization of 759 in exponential form is:

759 = 3¹ × 11¹ × 23¹

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 759

List of positive integer factors of 759 that divides 748 without a remainder.

1, 3, 11, 23, 33, 69, 253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 748 and 759. The biggest common factor number is the GCF number.
So the greatest common factor 748 and 759 is 11.

Also check out the Least Common Multiple of 748 and 759