What is the Greatest Common Factor of 728 and 742?

Greatest common factor (GCF) of 728 and 742 is 14.

GCF(728,742) = 14

We will now calculate the prime factors of 728 and 742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 728 and 742.

How to find the GCF of 728 and 742?

We will first find the prime factorization of 728 and 742. After we will calculate the factors of 728 and 742 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 742

Prime factors of 742 are 2, 7, 53. Prime factorization of 742 in exponential form is:

742 = 2¹ × 7¹ × 53¹

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 742

List of positive integer factors of 742 that divides 728 without a remainder.

1, 2, 7, 14, 53, 106, 371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 728 and 742. The biggest common factor number is the GCF number.
So the greatest common factor 728 and 742 is 14.

Also check out the Least Common Multiple of 728 and 742