What is the Greatest Common Factor of 31749 and 31764?

Greatest common factor (GCF) of 31749 and 31764 is 3.

GCF(31749,31764) = 3

We will now calculate the prime factors of 31749 and 31764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31749 and 31764.

How to find the GCF of 31749 and 31764?

We will first find the prime factorization of 31749 and 31764. After we will calculate the factors of 31749 and 31764 and find the biggest common factor number .

Step-1: Prime Factorization of 31749

Prime factors of 31749 are 3, 19, 557. Prime factorization of 31749 in exponential form is:

31749 = 3¹ × 19¹ × 557¹

Step-2: Prime Factorization of 31764

Prime factors of 31764 are 2, 3, 2647. Prime factorization of 31764 in exponential form is:

31764 = 2² × 3¹ × 2647¹

Step-3: Factors of 31749

List of positive integer factors of 31749 that divides 31749 without a remainder.

1, 3, 19, 57, 557, 1671, 10583

Step-4: Factors of 31764

List of positive integer factors of 31764 that divides 31749 without a remainder.

1, 2, 3, 4, 6, 12, 2647, 5294, 7941, 10588, 15882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31749 and 31764. The biggest common factor number is the GCF number.
So the greatest common factor 31749 and 31764 is 3.

Also check out the Least Common Multiple of 31749 and 31764