What is the Greatest Common Factor of 732 and 748?

Greatest common factor (GCF) of 732 and 748 is 4.

GCF(732,748) = 4

We will now calculate the prime factors of 732 and 748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 732 and 748.

How to find the GCF of 732 and 748?

We will first find the prime factorization of 732 and 748. After we will calculate the factors of 732 and 748 and find the biggest common factor number .

Step-1: Prime Factorization of 732

Prime factors of 732 are 2, 3, 61. Prime factorization of 732 in exponential form is:

732 = 2² × 3¹ × 61¹

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 732

List of positive integer factors of 732 that divides 732 without a remainder.

1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366

Step-4: Factors of 748

List of positive integer factors of 748 that divides 732 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 732 and 748. The biggest common factor number is the GCF number.
So the greatest common factor 732 and 748 is 4.

Also check out the Least Common Multiple of 732 and 748