What is the Greatest Common Factor of 38880 and 38889?

Greatest common factor (GCF) of 38880 and 38889 is 9.

GCF(38880,38889) = 9

We will now calculate the prime factors of 38880 and 38889, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38880 and 38889.

How to find the GCF of 38880 and 38889?

We will first find the prime factorization of 38880 and 38889. After we will calculate the factors of 38880 and 38889 and find the biggest common factor number .

Step-1: Prime Factorization of 38880

Prime factors of 38880 are 2, 3, 5. Prime factorization of 38880 in exponential form is:

38880 = 2⁵ × 3⁵ × 5¹

Step-2: Prime Factorization of 38889

Prime factors of 38889 are 3, 29, 149. Prime factorization of 38889 in exponential form is:

38889 = 3² × 29¹ × 149¹

Step-3: Factors of 38880

List of positive integer factors of 38880 that divides 38880 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 216, 240, 243, 270, 288, 324, 360, 405, 432, 480, 486, 540, 648, 720, 810, 864, 972, 1080, 1215, 1296, 1440, 1620, 1944, 2160, 2430, 2592, 3240, 3888, 4320, 4860, 6480, 7776, 9720, 12960, 19440

Step-4: Factors of 38889

List of positive integer factors of 38889 that divides 38880 without a remainder.

1, 3, 9, 29, 87, 149, 261, 447, 1341, 4321, 12963

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38880 and 38889. The biggest common factor number is the GCF number.
So the greatest common factor 38880 and 38889 is 9.

Also check out the Least Common Multiple of 38880 and 38889