What is the Greatest Common Factor of 59940 and 59949?

Greatest common factor (GCF) of 59940 and 59949 is 9.

GCF(59940,59949) = 9

We will now calculate the prime factors of 59940 and 59949, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59940 and 59949.

How to find the GCF of 59940 and 59949?

We will first find the prime factorization of 59940 and 59949. After we will calculate the factors of 59940 and 59949 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 59949

Prime factors of 59949 are 3, 6661. Prime factorization of 59949 in exponential form is:

59949 = 3² × 6661¹

Step-3: Factors of 59940

List of positive integer factors of 59940 that divides 59940 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

Step-4: Factors of 59949

List of positive integer factors of 59949 that divides 59940 without a remainder.

1, 3, 9, 6661, 19983

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59940 and 59949. The biggest common factor number is the GCF number.
So the greatest common factor 59940 and 59949 is 9.

Also check out the Least Common Multiple of 59940 and 59949