What is the Greatest Common Factor of 17871 and 17880?

Greatest common factor (GCF) of 17871 and 17880 is 3.

GCF(17871,17880) = 3

We will now calculate the prime factors of 17871 and 17880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17871 and 17880.

How to find the GCF of 17871 and 17880?

We will first find the prime factorization of 17871 and 17880. After we will calculate the factors of 17871 and 17880 and find the biggest common factor number .

Step-1: Prime Factorization of 17871

Prime factors of 17871 are 3, 7, 23, 37. Prime factorization of 17871 in exponential form is:

17871 = 3¹ × 7¹ × 23¹ × 37¹

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 17871

List of positive integer factors of 17871 that divides 17871 without a remainder.

1, 3, 7, 21, 23, 37, 69, 111, 161, 259, 483, 777, 851, 2553, 5957

Step-4: Factors of 17880

List of positive integer factors of 17880 that divides 17871 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 17871 and 17880. The biggest common factor number is the GCF number.
So the greatest common factor 17871 and 17880 is 3.

Also check out the Least Common Multiple of 17871 and 17880