What is the Greatest Common Factor of 31008 and 31024?

Greatest common factor (GCF) of 31008 and 31024 is 16.

GCF(31008,31024) = 16

We will now calculate the prime factors of 31008 and 31024, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31008 and 31024.

How to find the GCF of 31008 and 31024?

We will first find the prime factorization of 31008 and 31024. After we will calculate the factors of 31008 and 31024 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 31024

Prime factors of 31024 are 2, 7, 277. Prime factorization of 31024 in exponential form is:

31024 = 2⁴ × 7¹ × 277¹

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 31024

List of positive integer factors of 31024 that divides 31008 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 277, 554, 1108, 1939, 2216, 3878, 4432, 7756, 15512

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31008 and 31024. The biggest common factor number is the GCF number.
So the greatest common factor 31008 and 31024 is 16.

Also check out the Least Common Multiple of 31008 and 31024