What is the Greatest Common Factor of 58725 and 58734?

Greatest common factor (GCF) of 58725 and 58734 is 9.

GCF(58725,58734) = 9

We will now calculate the prime factors of 58725 and 58734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58725 and 58734.

How to find the GCF of 58725 and 58734?

We will first find the prime factorization of 58725 and 58734. After we will calculate the factors of 58725 and 58734 and find the biggest common factor number .

Step-1: Prime Factorization of 58725

Prime factors of 58725 are 3, 5, 29. Prime factorization of 58725 in exponential form is:

58725 = 3⁴ × 5² × 29¹

Step-2: Prime Factorization of 58734

Prime factors of 58734 are 2, 3, 13, 251. Prime factorization of 58734 in exponential form is:

58734 = 2¹ × 3² × 13¹ × 251¹

Step-3: Factors of 58725

List of positive integer factors of 58725 that divides 58725 without a remainder.

1, 3, 5, 9, 15, 25, 27, 29, 45, 75, 81, 87, 135, 145, 225, 261, 405, 435, 675, 725, 783, 1305, 2025, 2175, 2349, 3915, 6525, 11745, 19575

Step-4: Factors of 58734

List of positive integer factors of 58734 that divides 58725 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234, 251, 502, 753, 1506, 2259, 3263, 4518, 6526, 9789, 19578, 29367

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58725 and 58734. The biggest common factor number is the GCF number.
So the greatest common factor 58725 and 58734 is 9.

Also check out the Least Common Multiple of 58725 and 58734