What is the Greatest Common Factor of 725 and 745?

Greatest common factor (GCF) of 725 and 745 is 5.

GCF(725,745) = 5

We will now calculate the prime factors of 725 and 745, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 725 and 745.

How to find the GCF of 725 and 745?

We will first find the prime factorization of 725 and 745. After we will calculate the factors of 725 and 745 and find the biggest common factor number .

Step-1: Prime Factorization of 725

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

725 = 5² × 29¹

Step-2: Prime Factorization of 745

Prime factors of 745 are 5, 149. Prime factorization of 745 in exponential form is:

745 = 5¹ × 149¹

Step-3: Factors of 725

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

1, 5, 25, 29, 145

Step-4: Factors of 745

List of positive integer factors of 745 that divides 725 without a remainder.

1, 5, 149

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 725 and 745. The biggest common factor number is the GCF number.
So the greatest common factor 725 and 745 is 5.

Also check out the Least Common Multiple of 725 and 745