What is the Greatest Common Factor of 31494 and 31509?

Greatest common factor (GCF) of 31494 and 31509 is 3.

GCF(31494,31509) = 3

We will now calculate the prime factors of 31494 and 31509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31494 and 31509.

How to find the GCF of 31494 and 31509?

We will first find the prime factorization of 31494 and 31509. After we will calculate the factors of 31494 and 31509 and find the biggest common factor number .

Step-1: Prime Factorization of 31494

Prime factors of 31494 are 2, 3, 29, 181. Prime factorization of 31494 in exponential form is:

31494 = 2¹ × 3¹ × 29¹ × 181¹

Step-2: Prime Factorization of 31509

Prime factors of 31509 are 3, 389. Prime factorization of 31509 in exponential form is:

31509 = 3⁴ × 389¹

Step-3: Factors of 31494

List of positive integer factors of 31494 that divides 31494 without a remainder.

1, 2, 3, 6, 29, 58, 87, 174, 181, 362, 543, 1086, 5249, 10498, 15747

Step-4: Factors of 31509

List of positive integer factors of 31509 that divides 31494 without a remainder.

1, 3, 9, 27, 81, 389, 1167, 3501, 10503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31494 and 31509. The biggest common factor number is the GCF number.
So the greatest common factor 31494 and 31509 is 3.

Also check out the Least Common Multiple of 31494 and 31509