What is the Greatest Common Factor of 31644 and 31654?

Greatest common factor (GCF) of 31644 and 31654 is 2.

GCF(31644,31654) = 2

We will now calculate the prime factors of 31644 and 31654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31644 and 31654.

How to find the GCF of 31644 and 31654?

We will first find the prime factorization of 31644 and 31654. After we will calculate the factors of 31644 and 31654 and find the biggest common factor number .

Step-1: Prime Factorization of 31644

Prime factors of 31644 are 2, 3, 293. Prime factorization of 31644 in exponential form is:

31644 = 2² × 3³ × 293¹

Step-2: 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-3: Factors of 31644

List of positive integer factors of 31644 that divides 31644 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 293, 586, 879, 1172, 1758, 2637, 3516, 5274, 7911, 10548, 15822

Step-4: Factors of 31654

List of positive integer factors of 31654 that divides 31644 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31644 and 31654. The biggest common factor number is the GCF number.
So the greatest common factor 31644 and 31654 is 2.

Also check out the Least Common Multiple of 31644 and 31654