What is the Greatest Common Factor of 15969 and 15984?

Greatest common factor (GCF) of 15969 and 15984 is 3.

GCF(15969,15984) = 3

We will now calculate the prime factors of 15969 and 15984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15969 and 15984.

How to find the GCF of 15969 and 15984?

We will first find the prime factorization of 15969 and 15984. After we will calculate the factors of 15969 and 15984 and find the biggest common factor number .

Step-1: Prime Factorization of 15969

Prime factors of 15969 are 3, 5323. Prime factorization of 15969 in exponential form is:

15969 = 3¹ × 5323¹

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 15969

List of positive integer factors of 15969 that divides 15969 without a remainder.

1, 3, 5323

Step-4: Factors of 15984

List of positive integer factors of 15984 that divides 15969 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 15969 and 15984. The biggest common factor number is the GCF number.
So the greatest common factor 15969 and 15984 is 3.

Also check out the Least Common Multiple of 15969 and 15984