What is the Greatest Common Factor of 31997 and 32016?

Greatest common factor (GCF) of 31997 and 32016 is 1.

GCF(31997,32016) = 1

We will now calculate the prime factors of 31997 and 32016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31997 and 32016.

How to find the GCF of 31997 and 32016?

We will first find the prime factorization of 31997 and 32016. After we will calculate the factors of 31997 and 32016 and find the biggest common factor number .

Step-1: Prime Factorization of 31997

Prime factors of 31997 are 7, 653. Prime factorization of 31997 in exponential form is:

31997 = 7² × 653¹

Step-2: Prime Factorization of 32016

Prime factors of 32016 are 2, 3, 23, 29. Prime factorization of 32016 in exponential form is:

32016 = 2⁴ × 3¹ × 23¹ × 29¹

Step-3: Factors of 31997

List of positive integer factors of 31997 that divides 31997 without a remainder.

1, 7, 49, 653, 4571

Step-4: Factors of 32016

List of positive integer factors of 32016 that divides 31997 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 29, 46, 48, 58, 69, 87, 92, 116, 138, 174, 184, 232, 276, 348, 368, 464, 552, 667, 696, 1104, 1334, 1392, 2001, 2668, 4002, 5336, 8004, 10672, 16008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31997 and 32016. The biggest common factor number is the GCF number.
So the greatest common factor 31997 and 32016 is 1.

Also check out the Least Common Multiple of 31997 and 32016