What is the Greatest Common Factor of 59952 and 59964?

Greatest common factor (GCF) of 59952 and 59964 is 12.

GCF(59952,59964) = 12

We will now calculate the prime factors of 59952 and 59964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59952 and 59964.

How to find the GCF of 59952 and 59964?

We will first find the prime factorization of 59952 and 59964. After we will calculate the factors of 59952 and 59964 and find the biggest common factor number .

Step-1: Prime Factorization of 59952

Prime factors of 59952 are 2, 3, 1249. Prime factorization of 59952 in exponential form is:

59952 = 2⁴ × 3¹ × 1249¹

Step-2: Prime Factorization of 59964

Prime factors of 59964 are 2, 3, 19, 263. Prime factorization of 59964 in exponential form is:

59964 = 2² × 3¹ × 19¹ × 263¹

Step-3: Factors of 59952

List of positive integer factors of 59952 that divides 59952 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1249, 2498, 3747, 4996, 7494, 9992, 14988, 19984, 29976

Step-4: Factors of 59964

List of positive integer factors of 59964 that divides 59952 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 263, 526, 789, 1052, 1578, 3156, 4997, 9994, 14991, 19988, 29982

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59952 and 59964. The biggest common factor number is the GCF number.
So the greatest common factor 59952 and 59964 is 12.

Also check out the Least Common Multiple of 59952 and 59964