What is the Greatest Common Factor of 728 and 736?

Greatest common factor (GCF) of 728 and 736 is 8.

GCF(728,736) = 8

We will now calculate the prime factors of 728 and 736, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 728 and 736.

How to find the GCF of 728 and 736?

We will first find the prime factorization of 728 and 736. After we will calculate the factors of 728 and 736 and find the biggest common factor number .

Step-1: Prime Factorization of 728

Prime factors of 728 are 2, 7, 13. Prime factorization of 728 in exponential form is:

728 = 2³ × 7¹ × 13¹

Step-2: Prime Factorization of 736

Prime factors of 736 are 2, 23. Prime factorization of 736 in exponential form is:

736 = 2⁵ × 23¹

Step-3: Factors of 728

List of positive integer factors of 728 that divides 728 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364

Step-4: Factors of 736

List of positive integer factors of 736 that divides 728 without a remainder.

1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 728 and 736. The biggest common factor number is the GCF number.
So the greatest common factor 728 and 736 is 8.

Also check out the Least Common Multiple of 728 and 736