What is the Greatest Common Factor of 31654 and 31674?

Greatest common factor (GCF) of 31654 and 31674 is 2.

GCF(31654,31674) = 2

We will now calculate the prime factors of 31654 and 31674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31654 and 31674.

How to find the GCF of 31654 and 31674?

We will first find the prime factorization of 31654 and 31674. After we will calculate the factors of 31654 and 31674 and find the biggest common factor number .

Step-1: Prime Factorization of 31654

Prime factors of 31654 are 2, 7, 17, 19. Prime factorization of 31654 in exponential form is:

31654 = 2¹ × 7² × 17¹ × 19¹

Step-2: Prime Factorization of 31674

Prime factors of 31674 are 2, 3, 5279. Prime factorization of 31674 in exponential form is:

31674 = 2¹ × 3¹ × 5279¹

Step-3: Factors of 31654

List of positive integer factors of 31654 that divides 31654 without a remainder.

1, 2, 7, 14, 17, 19, 34, 38, 49, 98, 119, 133, 238, 266, 323, 646, 833, 931, 1666, 1862, 2261, 4522, 15827

Step-4: Factors of 31674

List of positive integer factors of 31674 that divides 31654 without a remainder.

1, 2, 3, 6, 5279, 10558, 15837

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31654 and 31674. The biggest common factor number is the GCF number.
So the greatest common factor 31654 and 31674 is 2.

Also check out the Least Common Multiple of 31654 and 31674