What is the Greatest Common Factor of 748 and 754?

Greatest common factor (GCF) of 748 and 754 is 2.

GCF(748,754) = 2

We will now calculate the prime factors of 748 and 754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 748 and 754.

How to find the GCF of 748 and 754?

We will first find the prime factorization of 748 and 754. After we will calculate the factors of 748 and 754 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 754

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

754 = 2¹ × 13¹ × 29¹

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 754

List of positive integer factors of 754 that divides 748 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 748 and 754. The biggest common factor number is the GCF number.
So the greatest common factor 748 and 754 is 2.

Also check out the Least Common Multiple of 748 and 754