What is the Greatest Common Factor of 59925 and 59940?

Greatest common factor (GCF) of 59925 and 59940 is 15.

GCF(59925,59940) = 15

We will now calculate the prime factors of 59925 and 59940, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59925 and 59940.

How to find the GCF of 59925 and 59940?

We will first find the prime factorization of 59925 and 59940. After we will calculate the factors of 59925 and 59940 and find the biggest common factor number .

Step-1: Prime Factorization of 59925

Prime factors of 59925 are 3, 5, 17, 47. Prime factorization of 59925 in exponential form is:

59925 = 3¹ × 5² × 17¹ × 47¹

Step-2: Prime Factorization of 59940

Prime factors of 59940 are 2, 3, 5, 37. Prime factorization of 59940 in exponential form is:

59940 = 2² × 3⁴ × 5¹ × 37¹

Step-3: Factors of 59925

List of positive integer factors of 59925 that divides 59925 without a remainder.

1, 3, 5, 15, 17, 25, 47, 51, 75, 85, 141, 235, 255, 425, 705, 799, 1175, 1275, 2397, 3525, 3995, 11985, 19975

Step-4: Factors of 59940

List of positive integer factors of 59940 that divides 59925 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 37, 45, 54, 60, 74, 81, 90, 108, 111, 135, 148, 162, 180, 185, 222, 270, 324, 333, 370, 405, 444, 540, 555, 666, 740, 810, 999, 1110, 1332, 1620, 1665, 1998, 2220, 2997, 3330, 3996, 4995, 5994, 6660, 9990, 11988, 14985, 19980, 29970

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59925 and 59940. The biggest common factor number is the GCF number.
So the greatest common factor 59925 and 59940 is 15.

Also check out the Least Common Multiple of 59925 and 59940