What is the Greatest Common Factor of 30991 and 31008?

Greatest common factor (GCF) of 30991 and 31008 is 17.

GCF(30991,31008) = 17

We will now calculate the prime factors of 30991 and 31008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30991 and 31008.

How to find the GCF of 30991 and 31008?

We will first find the prime factorization of 30991 and 31008. After we will calculate the factors of 30991 and 31008 and find the biggest common factor number .

Step-1: Prime Factorization of 30991

Prime factors of 30991 are 17, 1823. Prime factorization of 30991 in exponential form is:

30991 = 17¹ × 1823¹

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 30991

List of positive integer factors of 30991 that divides 30991 without a remainder.

1, 17, 1823

Step-4: Factors of 31008

List of positive integer factors of 31008 that divides 30991 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 30991 and 31008. The biggest common factor number is the GCF number.
So the greatest common factor 30991 and 31008 is 17.

Also check out the Least Common Multiple of 30991 and 31008