What is the Greatest Common Factor of 39984 and 39996?

Greatest common factor (GCF) of 39984 and 39996 is 12.

GCF(39984,39996) = 12

We will now calculate the prime factors of 39984 and 39996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39984 and 39996.

How to find the GCF of 39984 and 39996?

We will first find the prime factorization of 39984 and 39996. After we will calculate the factors of 39984 and 39996 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39996

Prime factors of 39996 are 2, 3, 11, 101. Prime factorization of 39996 in exponential form is:

39996 = 2² × 3² × 11¹ × 101¹

Step-3: Factors of 39984

List of positive integer factors of 39984 that divides 39984 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

Step-4: Factors of 39996

List of positive integer factors of 39996 that divides 39984 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 101, 132, 198, 202, 303, 396, 404, 606, 909, 1111, 1212, 1818, 2222, 3333, 3636, 4444, 6666, 9999, 13332, 19998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39984 and 39996. The biggest common factor number is the GCF number.
So the greatest common factor 39984 and 39996 is 12.

Also check out the Least Common Multiple of 39984 and 39996