What is the Greatest Common Factor of 39975 and 39984?

Greatest common factor (GCF) of 39975 and 39984 is 3.

GCF(39975,39984) = 3

We will now calculate the prime factors of 39975 and 39984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39975 and 39984.

How to find the GCF of 39975 and 39984?

We will first find the prime factorization of 39975 and 39984. After we will calculate the factors of 39975 and 39984 and find the biggest common factor number .

Step-1: Prime Factorization of 39975

Prime factors of 39975 are 3, 5, 13, 41. Prime factorization of 39975 in exponential form is:

39975 = 3¹ × 5² × 13¹ × 41¹

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 39975

List of positive integer factors of 39975 that divides 39975 without a remainder.

1, 3, 5, 13, 15, 25, 39, 41, 65, 75, 123, 195, 205, 325, 533, 615, 975, 1025, 1599, 2665, 3075, 7995, 13325

Step-4: Factors of 39984

List of positive integer factors of 39984 that divides 39975 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 39975 and 39984. The biggest common factor number is the GCF number.
So the greatest common factor 39975 and 39984 is 3.

Also check out the Least Common Multiple of 39975 and 39984