What is the Greatest Common Factor of 31993 and 32006?

Greatest common factor (GCF) of 31993 and 32006 is 13.

GCF(31993,32006) = 13

We will now calculate the prime factors of 31993 and 32006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31993 and 32006.

How to find the GCF of 31993 and 32006?

We will first find the prime factorization of 31993 and 32006. After we will calculate the factors of 31993 and 32006 and find the biggest common factor number .

Step-1: Prime Factorization of 31993

Prime factors of 31993 are 13, 23, 107. Prime factorization of 31993 in exponential form is:

31993 = 13¹ × 23¹ × 107¹

Step-2: Prime Factorization of 32006

Prime factors of 32006 are 2, 13, 1231. Prime factorization of 32006 in exponential form is:

32006 = 2¹ × 13¹ × 1231¹

Step-3: Factors of 31993

List of positive integer factors of 31993 that divides 31993 without a remainder.

1, 13, 23, 107, 299, 1391, 2461

Step-4: Factors of 32006

List of positive integer factors of 32006 that divides 31993 without a remainder.

1, 2, 13, 26, 1231, 2462, 16003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31993 and 32006. The biggest common factor number is the GCF number.
So the greatest common factor 31993 and 32006 is 13.

Also check out the Least Common Multiple of 31993 and 32006