What is the Greatest Common Factor of 31008 and 31020?

Greatest common factor (GCF) of 31008 and 31020 is 12.

GCF(31008,31020) = 12

We will now calculate the prime factors of 31008 and 31020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31008 and 31020.

How to find the GCF of 31008 and 31020?

We will first find the prime factorization of 31008 and 31020. After we will calculate the factors of 31008 and 31020 and find the biggest common factor number .

Step-1: Prime Factorization of 31008

Prime factors of 31008 are 2, 3, 17, 19. Prime factorization of 31008 in exponential form is:

31008 = 2⁵ × 3¹ × 17¹ × 19¹

Step-2: Prime Factorization of 31020

Prime factors of 31020 are 2, 3, 5, 11, 47. Prime factorization of 31020 in exponential form is:

31020 = 2² × 3¹ × 5¹ × 11¹ × 47¹

Step-3: Factors of 31008

List of positive integer factors of 31008 that divides 31008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 19, 24, 32, 34, 38, 48, 51, 57, 68, 76, 96, 102, 114, 136, 152, 204, 228, 272, 304, 323, 408, 456, 544, 608, 646, 816, 912, 969, 1292, 1632, 1824, 1938, 2584, 3876, 5168, 7752, 10336, 15504

Step-4: Factors of 31020

List of positive integer factors of 31020 that divides 31008 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 47, 55, 60, 66, 94, 110, 132, 141, 165, 188, 220, 235, 282, 330, 470, 517, 564, 660, 705, 940, 1034, 1410, 1551, 2068, 2585, 2820, 3102, 5170, 6204, 7755, 10340, 15510

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31008 and 31020. The biggest common factor number is the GCF number.
So the greatest common factor 31008 and 31020 is 12.

Also check out the Least Common Multiple of 31008 and 31020