What is the Greatest Common Factor of 30992 and 31008?

Greatest common factor (GCF) of 30992 and 31008 is 16.

GCF(30992,31008) = 16

We will now calculate the prime factors of 30992 and 31008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30992 and 31008.

How to find the GCF of 30992 and 31008?

We will first find the prime factorization of 30992 and 31008. After we will calculate the factors of 30992 and 31008 and find the biggest common factor number .

Step-1: Prime Factorization of 30992

Prime factors of 30992 are 2, 13, 149. Prime factorization of 30992 in exponential form is:

30992 = 2⁴ × 13¹ × 149¹

Step-2: 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-3: Factors of 30992

List of positive integer factors of 30992 that divides 30992 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 149, 208, 298, 596, 1192, 1937, 2384, 3874, 7748, 15496

Step-4: Factors of 31008

List of positive integer factors of 31008 that divides 30992 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30992 and 31008. The biggest common factor number is the GCF number.
So the greatest common factor 30992 and 31008 is 16.

Also check out the Least Common Multiple of 30992 and 31008