What is the Greatest Common Factor of 30992 and 31006?

Greatest common factor (GCF) of 30992 and 31006 is 2.

GCF(30992,31006) = 2

We will now calculate the prime factors of 30992 and 31006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30992 and 31006.

How to find the GCF of 30992 and 31006?

We will first find the prime factorization of 30992 and 31006. After we will calculate the factors of 30992 and 31006 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 31006

Prime factors of 31006 are 2, 37, 419. Prime factorization of 31006 in exponential form is:

31006 = 2¹ × 37¹ × 419¹

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 31006

List of positive integer factors of 31006 that divides 30992 without a remainder.

1, 2, 37, 74, 419, 838, 15503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30992 and 31006. The biggest common factor number is the GCF number.
So the greatest common factor 30992 and 31006 is 2.

Also check out the Least Common Multiple of 30992 and 31006