What is the Greatest Common Factor of 710 and 725?

Greatest common factor (GCF) of 710 and 725 is 5.

GCF(710,725) = 5

We will now calculate the prime factors of 710 and 725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 710 and 725.

How to find the GCF of 710 and 725?

We will first find the prime factorization of 710 and 725. After we will calculate the factors of 710 and 725 and find the biggest common factor number .

Step-1: Prime Factorization of 710

Prime factors of 710 are 2, 5, 71. Prime factorization of 710 in exponential form is:

710 = 2¹ × 5¹ × 71¹

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 710

List of positive integer factors of 710 that divides 710 without a remainder.

1, 2, 5, 10, 71, 142, 355

Step-4: Factors of 725

List of positive integer factors of 725 that divides 710 without a remainder.

1, 5, 25, 29, 145

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 710 and 725. The biggest common factor number is the GCF number.
So the greatest common factor 710 and 725 is 5.

Also check out the Least Common Multiple of 710 and 725