What is the Greatest Common Factor of 31947 and 31965?

Greatest common factor (GCF) of 31947 and 31965 is 3.

GCF(31947,31965) = 3

We will now calculate the prime factors of 31947 and 31965, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31947 and 31965.

How to find the GCF of 31947 and 31965?

We will first find the prime factorization of 31947 and 31965. After we will calculate the factors of 31947 and 31965 and find the biggest common factor number .

Step-1: Prime Factorization of 31947

Prime factors of 31947 are 3, 23, 463. Prime factorization of 31947 in exponential form is:

31947 = 3¹ × 23¹ × 463¹

Step-2: Prime Factorization of 31965

Prime factors of 31965 are 3, 5, 2131. Prime factorization of 31965 in exponential form is:

31965 = 3¹ × 5¹ × 2131¹

Step-3: Factors of 31947

List of positive integer factors of 31947 that divides 31947 without a remainder.

1, 3, 23, 69, 463, 1389, 10649

Step-4: Factors of 31965

List of positive integer factors of 31965 that divides 31947 without a remainder.

1, 3, 5, 15, 2131, 6393, 10655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31947 and 31965. The biggest common factor number is the GCF number.
So the greatest common factor 31947 and 31965 is 3.

Also check out the Least Common Multiple of 31947 and 31965