What is the Greatest Common Factor of 45972 and 45984?

Greatest common factor (GCF) of 45972 and 45984 is 12.

GCF(45972,45984) = 12

We will now calculate the prime factors of 45972 and 45984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45972 and 45984.

How to find the GCF of 45972 and 45984?

We will first find the prime factorization of 45972 and 45984. After we will calculate the factors of 45972 and 45984 and find the biggest common factor number .

Step-1: Prime Factorization of 45972

Prime factors of 45972 are 2, 3, 1277. Prime factorization of 45972 in exponential form is:

45972 = 2² × 3² × 1277¹

Step-2: Prime Factorization of 45984

Prime factors of 45984 are 2, 3, 479. Prime factorization of 45984 in exponential form is:

45984 = 2⁵ × 3¹ × 479¹

Step-3: Factors of 45972

List of positive integer factors of 45972 that divides 45972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1277, 2554, 3831, 5108, 7662, 11493, 15324, 22986

Step-4: Factors of 45984

List of positive integer factors of 45984 that divides 45972 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 479, 958, 1437, 1916, 2874, 3832, 5748, 7664, 11496, 15328, 22992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45972 and 45984. The biggest common factor number is the GCF number.
So the greatest common factor 45972 and 45984 is 12.

Also check out the Least Common Multiple of 45972 and 45984