What is the Greatest Common Factor of 748 and 758?

Greatest common factor (GCF) of 748 and 758 is 2.

GCF(748,758) = 2

We will now calculate the prime factors of 748 and 758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 748 and 758.

How to find the GCF of 748 and 758?

We will first find the prime factorization of 748 and 758. After we will calculate the factors of 748 and 758 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 758

Prime factors of 758 are 2, 379. Prime factorization of 758 in exponential form is:

758 = 2¹ × 379¹

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 758

List of positive integer factors of 758 that divides 748 without a remainder.

1, 2, 379

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 748 and 758. The biggest common factor number is the GCF number.
So the greatest common factor 748 and 758 is 2.

Also check out the Least Common Multiple of 748 and 758