What is the Greatest Common Factor of 17880 and 17900?

Greatest common factor (GCF) of 17880 and 17900 is 20.

GCF(17880,17900) = 20

We will now calculate the prime factors of 17880 and 17900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17880 and 17900.

How to find the GCF of 17880 and 17900?

We will first find the prime factorization of 17880 and 17900. After we will calculate the factors of 17880 and 17900 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17900

Prime factors of 17900 are 2, 5, 179. Prime factorization of 17900 in exponential form is:

17900 = 2² × 5² × 179¹

Step-3: Factors of 17880

List of positive integer factors of 17880 that divides 17880 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

Step-4: Factors of 17900

List of positive integer factors of 17900 that divides 17880 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 179, 358, 716, 895, 1790, 3580, 4475, 8950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17880 and 17900. The biggest common factor number is the GCF number.
So the greatest common factor 17880 and 17900 is 20.

Also check out the Least Common Multiple of 17880 and 17900