What is the Greatest Common Factor of 15975 and 15984?

Greatest common factor (GCF) of 15975 and 15984 is 9.

GCF(15975,15984) = 9

We will now calculate the prime factors of 15975 and 15984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15975 and 15984.

How to find the GCF of 15975 and 15984?

We will first find the prime factorization of 15975 and 15984. After we will calculate the factors of 15975 and 15984 and find the biggest common factor number .

Step-1: Prime Factorization of 15975

Prime factors of 15975 are 3, 5, 71. Prime factorization of 15975 in exponential form is:

15975 = 3² × 5² × 71¹

Step-2: Prime Factorization of 15984

Prime factors of 15984 are 2, 3, 37. Prime factorization of 15984 in exponential form is:

15984 = 2⁴ × 3³ × 37¹

Step-3: Factors of 15975

List of positive integer factors of 15975 that divides 15975 without a remainder.

1, 3, 5, 9, 15, 25, 45, 71, 75, 213, 225, 355, 639, 1065, 1775, 3195, 5325

Step-4: Factors of 15984

List of positive integer factors of 15984 that divides 15975 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 37, 48, 54, 72, 74, 108, 111, 144, 148, 216, 222, 296, 333, 432, 444, 592, 666, 888, 999, 1332, 1776, 1998, 2664, 3996, 5328, 7992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15975 and 15984. The biggest common factor number is the GCF number.
So the greatest common factor 15975 and 15984 is 9.

Also check out the Least Common Multiple of 15975 and 15984