What is the Greatest Common Factor of 17865 and 17880?

Greatest common factor (GCF) of 17865 and 17880 is 15.

GCF(17865,17880) = 15

We will now calculate the prime factors of 17865 and 17880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17865 and 17880.

How to find the GCF of 17865 and 17880?

We will first find the prime factorization of 17865 and 17880. After we will calculate the factors of 17865 and 17880 and find the biggest common factor number .

Step-1: Prime Factorization of 17865

Prime factors of 17865 are 3, 5, 397. Prime factorization of 17865 in exponential form is:

17865 = 3² × 5¹ × 397¹

Step-2: Prime Factorization of 17880

Prime factors of 17880 are 2, 3, 5, 149. Prime factorization of 17880 in exponential form is:

17880 = 2³ × 3¹ × 5¹ × 149¹

Step-3: Factors of 17865

List of positive integer factors of 17865 that divides 17865 without a remainder.

1, 3, 5, 9, 15, 45, 397, 1191, 1985, 3573, 5955

Step-4: Factors of 17880

List of positive integer factors of 17880 that divides 17865 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 149, 298, 447, 596, 745, 894, 1192, 1490, 1788, 2235, 2980, 3576, 4470, 5960, 8940

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17865 and 17880. The biggest common factor number is the GCF number.
So the greatest common factor 17865 and 17880 is 15.

Also check out the Least Common Multiple of 17865 and 17880