What is the Greatest Common Factor of 39972 and 39984?

Greatest common factor (GCF) of 39972 and 39984 is 12.

GCF(39972,39984) = 12

We will now calculate the prime factors of 39972 and 39984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39972 and 39984.

How to find the GCF of 39972 and 39984?

We will first find the prime factorization of 39972 and 39984. After we will calculate the factors of 39972 and 39984 and find the biggest common factor number .

Step-1: Prime Factorization of 39972

Prime factors of 39972 are 2, 3, 3331. Prime factorization of 39972 in exponential form is:

39972 = 2² × 3¹ × 3331¹

Step-2: Prime Factorization of 39984

Prime factors of 39984 are 2, 3, 7, 17. Prime factorization of 39984 in exponential form is:

39984 = 2⁴ × 3¹ × 7² × 17¹

Step-3: Factors of 39972

List of positive integer factors of 39972 that divides 39972 without a remainder.

1, 2, 3, 4, 6, 12, 3331, 6662, 9993, 13324, 19986

Step-4: Factors of 39984

List of positive integer factors of 39984 that divides 39972 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42, 48, 49, 51, 56, 68, 84, 98, 102, 112, 119, 136, 147, 168, 196, 204, 238, 272, 294, 336, 357, 392, 408, 476, 588, 714, 784, 816, 833, 952, 1176, 1428, 1666, 1904, 2352, 2499, 2856, 3332, 4998, 5712, 6664, 9996, 13328, 19992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39972 and 39984. The biggest common factor number is the GCF number.
So the greatest common factor 39972 and 39984 is 12.

Also check out the Least Common Multiple of 39972 and 39984