What is the Greatest Common Factor of 75960 and 75972?

Greatest common factor (GCF) of 75960 and 75972 is 12.

GCF(75960,75972) = 12

We will now calculate the prime factors of 75960 and 75972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75960 and 75972.

How to find the GCF of 75960 and 75972?

We will first find the prime factorization of 75960 and 75972. After we will calculate the factors of 75960 and 75972 and find the biggest common factor number .

Step-1: Prime Factorization of 75960

Prime factors of 75960 are 2, 3, 5, 211. Prime factorization of 75960 in exponential form is:

75960 = 2³ × 3² × 5¹ × 211¹

Step-2: Prime Factorization of 75972

Prime factors of 75972 are 2, 3, 13, 487. Prime factorization of 75972 in exponential form is:

75972 = 2² × 3¹ × 13¹ × 487¹

Step-3: Factors of 75960

List of positive integer factors of 75960 that divides 75960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 211, 360, 422, 633, 844, 1055, 1266, 1688, 1899, 2110, 2532, 3165, 3798, 4220, 5064, 6330, 7596, 8440, 9495, 12660, 15192, 18990, 25320, 37980

Step-4: Factors of 75972

List of positive integer factors of 75972 that divides 75960 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 487, 974, 1461, 1948, 2922, 5844, 6331, 12662, 18993, 25324, 37986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75960 and 75972. The biggest common factor number is the GCF number.
So the greatest common factor 75960 and 75972 is 12.

Also check out the Least Common Multiple of 75960 and 75972