What is the Greatest Common Factor of 17949 and 17964?

Greatest common factor (GCF) of 17949 and 17964 is 3.

GCF(17949,17964) = 3

We will now calculate the prime factors of 17949 and 17964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17949 and 17964.

How to find the GCF of 17949 and 17964?

We will first find the prime factorization of 17949 and 17964. After we will calculate the factors of 17949 and 17964 and find the biggest common factor number .

Step-1: Prime Factorization of 17949

Prime factors of 17949 are 3, 31, 193. Prime factorization of 17949 in exponential form is:

17949 = 3¹ × 31¹ × 193¹

Step-2: Prime Factorization of 17964

Prime factors of 17964 are 2, 3, 499. Prime factorization of 17964 in exponential form is:

17964 = 2² × 3² × 499¹

Step-3: Factors of 17949

List of positive integer factors of 17949 that divides 17949 without a remainder.

1, 3, 31, 93, 193, 579, 5983

Step-4: Factors of 17964

List of positive integer factors of 17964 that divides 17949 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 499, 998, 1497, 1996, 2994, 4491, 5988, 8982

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17949 and 17964. The biggest common factor number is the GCF number.
So the greatest common factor 17949 and 17964 is 3.

Also check out the Least Common Multiple of 17949 and 17964