What is the Greatest Common Factor of 731 and 748?

Greatest common factor (GCF) of 731 and 748 is 17.

GCF(731,748) = 17

We will now calculate the prime factors of 731 and 748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 731 and 748.

How to find the GCF of 731 and 748?

We will first find the prime factorization of 731 and 748. After we will calculate the factors of 731 and 748 and find the biggest common factor number .

Step-1: Prime Factorization of 731

Prime factors of 731 are 17, 43. Prime factorization of 731 in exponential form is:

731 = 17¹ × 43¹

Step-2: 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-3: Factors of 731

List of positive integer factors of 731 that divides 731 without a remainder.

1, 17, 43

Step-4: Factors of 748

List of positive integer factors of 748 that divides 731 without a remainder.

1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 731 and 748. The biggest common factor number is the GCF number.
So the greatest common factor 731 and 748 is 17.

Also check out the Least Common Multiple of 731 and 748