What is the Greatest Common Factor of 15965 and 15984?

Greatest common factor (GCF) of 15965 and 15984 is 1.

GCF(15965,15984) = 1

We will now calculate the prime factors of 15965 and 15984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15965 and 15984.

How to find the GCF of 15965 and 15984?

We will first find the prime factorization of 15965 and 15984. After we will calculate the factors of 15965 and 15984 and find the biggest common factor number .

Step-1: Prime Factorization of 15965

Prime factors of 15965 are 5, 31, 103. Prime factorization of 15965 in exponential form is:

15965 = 5¹ × 31¹ × 103¹

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 15965

List of positive integer factors of 15965 that divides 15965 without a remainder.

1, 5, 31, 103, 155, 515, 3193

Step-4: Factors of 15984

List of positive integer factors of 15984 that divides 15965 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 15965 and 15984. The biggest common factor number is the GCF number.
So the greatest common factor 15965 and 15984 is 1.

Also check out the Least Common Multiple of 15965 and 15984