What is the Greatest Common Factor of 31641 and 31659?

Greatest common factor (GCF) of 31641 and 31659 is 3.

GCF(31641,31659) = 3

We will now calculate the prime factors of 31641 and 31659, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31641 and 31659.

How to find the GCF of 31641 and 31659?

We will first find the prime factorization of 31641 and 31659. After we will calculate the factors of 31641 and 31659 and find the biggest common factor number .

Step-1: Prime Factorization of 31641

Prime factors of 31641 are 3, 53, 199. Prime factorization of 31641 in exponential form is:

31641 = 3¹ × 53¹ × 199¹

Step-2: Prime Factorization of 31659

Prime factors of 31659 are 3, 61, 173. Prime factorization of 31659 in exponential form is:

31659 = 3¹ × 61¹ × 173¹

Step-3: Factors of 31641

List of positive integer factors of 31641 that divides 31641 without a remainder.

1, 3, 53, 159, 199, 597, 10547

Step-4: Factors of 31659

List of positive integer factors of 31659 that divides 31641 without a remainder.

1, 3, 61, 173, 183, 519, 10553

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31641 and 31659. The biggest common factor number is the GCF number.
So the greatest common factor 31641 and 31659 is 3.

Also check out the Least Common Multiple of 31641 and 31659