What is the Greatest Common Factor of 31008 and 31014?

Greatest common factor (GCF) of 31008 and 31014 is 6.

GCF(31008,31014) = 6

We will now calculate the prime factors of 31008 and 31014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31008 and 31014.

How to find the GCF of 31008 and 31014?

We will first find the prime factorization of 31008 and 31014. After we will calculate the factors of 31008 and 31014 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 31014

Prime factors of 31014 are 2, 3, 1723. Prime factorization of 31014 in exponential form is:

31014 = 2¹ × 3² × 1723¹

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 31014

List of positive integer factors of 31014 that divides 31008 without a remainder.

1, 2, 3, 6, 9, 18, 1723, 3446, 5169, 10338, 15507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31008 and 31014. The biggest common factor number is the GCF number.
So the greatest common factor 31008 and 31014 is 6.

Also check out the Least Common Multiple of 31008 and 31014