What is the Greatest Common Factor of 17880 and 17888?

Greatest common factor (GCF) of 17880 and 17888 is 8.

GCF(17880,17888) = 8

We will now calculate the prime factors of 17880 and 17888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17880 and 17888.

How to find the GCF of 17880 and 17888?

We will first find the prime factorization of 17880 and 17888. After we will calculate the factors of 17880 and 17888 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 17888

Prime factors of 17888 are 2, 13, 43. Prime factorization of 17888 in exponential form is:

17888 = 2⁵ × 13¹ × 43¹

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 17888

List of positive integer factors of 17888 that divides 17880 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 43, 52, 86, 104, 172, 208, 344, 416, 559, 688, 1118, 1376, 2236, 4472, 8944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17880 and 17888. The biggest common factor number is the GCF number.
So the greatest common factor 17880 and 17888 is 8.

Also check out the Least Common Multiple of 17880 and 17888