What is the Greatest Common Factor of 31989 and 32007?

Greatest common factor (GCF) of 31989 and 32007 is 3.

GCF(31989,32007) = 3

We will now calculate the prime factors of 31989 and 32007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31989 and 32007.

How to find the GCF of 31989 and 32007?

We will first find the prime factorization of 31989 and 32007. After we will calculate the factors of 31989 and 32007 and find the biggest common factor number .

Step-1: Prime Factorization of 31989

Prime factors of 31989 are 3, 10663. Prime factorization of 31989 in exponential form is:

31989 = 3¹ × 10663¹

Step-2: Prime Factorization of 32007

Prime factors of 32007 are 3, 47, 227. Prime factorization of 32007 in exponential form is:

32007 = 3¹ × 47¹ × 227¹

Step-3: Factors of 31989

List of positive integer factors of 31989 that divides 31989 without a remainder.

1, 3, 10663

Step-4: Factors of 32007

List of positive integer factors of 32007 that divides 31989 without a remainder.

1, 3, 47, 141, 227, 681, 10669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31989 and 32007. The biggest common factor number is the GCF number.
So the greatest common factor 31989 and 32007 is 3.

Also check out the Least Common Multiple of 31989 and 32007