What is the Greatest Common Factor of 725 and 737?

Greatest common factor (GCF) of 725 and 737 is 1.

GCF(725,737) = 1

We will now calculate the prime factors of 725 and 737, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 725 and 737.

How to find the GCF of 725 and 737?

We will first find the prime factorization of 725 and 737. After we will calculate the factors of 725 and 737 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 737

Prime factors of 737 are 11, 67. Prime factorization of 737 in exponential form is:

737 = 11¹ × 67¹

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 737

List of positive integer factors of 737 that divides 725 without a remainder.

1, 11, 67

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 725 and 737. The biggest common factor number is the GCF number.
So the greatest common factor 725 and 737 is 1.

Also check out the Least Common Multiple of 725 and 737