What is the Greatest Common Factor of 31974 and 31989?

Greatest common factor (GCF) of 31974 and 31989 is 3.

GCF(31974,31989) = 3

We will now calculate the prime factors of 31974 and 31989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31974 and 31989.

How to find the GCF of 31974 and 31989?

We will first find the prime factorization of 31974 and 31989. After we will calculate the factors of 31974 and 31989 and find the biggest common factor number .

Step-1: Prime Factorization of 31974

Prime factors of 31974 are 2, 3, 73. Prime factorization of 31974 in exponential form is:

31974 = 2¹ × 3¹ × 73²

Step-2: Prime Factorization of 31989

Prime factors of 31989 are 3, 10663. Prime factorization of 31989 in exponential form is:

31989 = 3¹ × 10663¹

Step-3: Factors of 31974

List of positive integer factors of 31974 that divides 31974 without a remainder.

1, 2, 3, 6, 73, 146, 219, 438, 5329, 10658, 15987

Step-4: Factors of 31989

List of positive integer factors of 31989 that divides 31974 without a remainder.

1, 3, 10663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31974 and 31989. The biggest common factor number is the GCF number.
So the greatest common factor 31974 and 31989 is 3.

Also check out the Least Common Multiple of 31974 and 31989