What is the Greatest Common Factor of 39984 and 39990?

Greatest common factor (GCF) of 39984 and 39990 is 6.

GCF(39984,39990) = 6

We will now calculate the prime factors of 39984 and 39990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39984 and 39990.

How to find the GCF of 39984 and 39990?

We will first find the prime factorization of 39984 and 39990. After we will calculate the factors of 39984 and 39990 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 39990

Prime factors of 39990 are 2, 3, 5, 31, 43. Prime factorization of 39990 in exponential form is:

39990 = 2¹ × 3¹ × 5¹ × 31¹ × 43¹

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 39990

List of positive integer factors of 39990 that divides 39984 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 31, 43, 62, 86, 93, 129, 155, 186, 215, 258, 310, 430, 465, 645, 930, 1290, 1333, 2666, 3999, 6665, 7998, 13330, 19995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39984 and 39990. The biggest common factor number is the GCF number.
So the greatest common factor 39984 and 39990 is 6.

Also check out the Least Common Multiple of 39984 and 39990