What is the Greatest Common Factor of 38880 and 38900?

Greatest common factor (GCF) of 38880 and 38900 is 20.

GCF(38880,38900) = 20

We will now calculate the prime factors of 38880 and 38900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38880 and 38900.

How to find the GCF of 38880 and 38900?

We will first find the prime factorization of 38880 and 38900. After we will calculate the factors of 38880 and 38900 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 38900

Prime factors of 38900 are 2, 5, 389. Prime factorization of 38900 in exponential form is:

38900 = 2² × 5² × 389¹

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 38900

List of positive integer factors of 38900 that divides 38880 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 389, 778, 1556, 1945, 3890, 7780, 9725, 19450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38880 and 38900. The biggest common factor number is the GCF number.
So the greatest common factor 38880 and 38900 is 20.

Also check out the Least Common Multiple of 38880 and 38900