What is the Greatest Common Factor of 31605 and 31614?

Greatest common factor (GCF) of 31605 and 31614 is 3.

GCF(31605,31614) = 3

We will now calculate the prime factors of 31605 and 31614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31605 and 31614.

How to find the GCF of 31605 and 31614?

We will first find the prime factorization of 31605 and 31614. After we will calculate the factors of 31605 and 31614 and find the biggest common factor number .

Step-1: Prime Factorization of 31605

Prime factors of 31605 are 3, 5, 7, 43. Prime factorization of 31605 in exponential form is:

31605 = 3¹ × 5¹ × 7² × 43¹

Step-2: Prime Factorization of 31614

Prime factors of 31614 are 2, 3, 11, 479. Prime factorization of 31614 in exponential form is:

31614 = 2¹ × 3¹ × 11¹ × 479¹

Step-3: Factors of 31605

List of positive integer factors of 31605 that divides 31605 without a remainder.

1, 3, 5, 7, 15, 21, 35, 43, 49, 105, 129, 147, 215, 245, 301, 645, 735, 903, 1505, 2107, 4515, 6321, 10535

Step-4: Factors of 31614

List of positive integer factors of 31614 that divides 31605 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 479, 958, 1437, 2874, 5269, 10538, 15807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31605 and 31614. The biggest common factor number is the GCF number.
So the greatest common factor 31605 and 31614 is 3.

Also check out the Least Common Multiple of 31605 and 31614