What is the Greatest Common Factor of 728 and 738?

Greatest common factor (GCF) of 728 and 738 is 2.

GCF(728,738) = 2

We will now calculate the prime factors of 728 and 738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 728 and 738.

How to find the GCF of 728 and 738?

We will first find the prime factorization of 728 and 738. After we will calculate the factors of 728 and 738 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 738

Prime factors of 738 are 2, 3, 41. Prime factorization of 738 in exponential form is:

738 = 2¹ × 3² × 41¹

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 738

List of positive integer factors of 738 that divides 728 without a remainder.

1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 728 and 738. The biggest common factor number is the GCF number.
So the greatest common factor 728 and 738 is 2.

Also check out the Least Common Multiple of 728 and 738