What is the Greatest Common Factor of 714 and 725?

Greatest common factor (GCF) of 714 and 725 is 1.

GCF(714,725) = 1

We will now calculate the prime factors of 714 and 725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 714 and 725.

How to find the GCF of 714 and 725?

We will first find the prime factorization of 714 and 725. After we will calculate the factors of 714 and 725 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 725

Prime factors of 725 are 5, 29. Prime factorization of 725 in exponential form is:

725 = 5² × 29¹

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 725

List of positive integer factors of 725 that divides 714 without a remainder.

1, 5, 25, 29, 145

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 714 and 725. The biggest common factor number is the GCF number.
So the greatest common factor 714 and 725 is 1.

Also check out the Least Common Multiple of 714 and 725