What is the Greatest Common Factor of 714 and 728?

Greatest common factor (GCF) of 714 and 728 is 14.

GCF(714,728) = 14

We will now calculate the prime factors of 714 and 728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 714 and 728.

How to find the GCF of 714 and 728?

We will first find the prime factorization of 714 and 728. After we will calculate the factors of 714 and 728 and find the biggest common factor number .

Step-1: Prime Factorization of 714

Prime factors of 714 are 2, 3, 7, 17. Prime factorization of 714 in exponential form is:

714 = 2¹ × 3¹ × 7¹ × 17¹

Step-2: 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-3: Factors of 714

List of positive integer factors of 714 that divides 714 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357

Step-4: Factors of 728

List of positive integer factors of 728 that divides 714 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 714 and 728. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 728 is 14.

Also check out the Least Common Multiple of 714 and 728