What is the Greatest Common Factor of 38872 and 38880?

Greatest common factor (GCF) of 38872 and 38880 is 8.

GCF(38872,38880) = 8

We will now calculate the prime factors of 38872 and 38880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38872 and 38880.

How to find the GCF of 38872 and 38880?

We will first find the prime factorization of 38872 and 38880. After we will calculate the factors of 38872 and 38880 and find the biggest common factor number .

Step-1: Prime Factorization of 38872

Prime factors of 38872 are 2, 43, 113. Prime factorization of 38872 in exponential form is:

38872 = 2³ × 43¹ × 113¹

Step-2: 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-3: Factors of 38872

List of positive integer factors of 38872 that divides 38872 without a remainder.

1, 2, 4, 8, 43, 86, 113, 172, 226, 344, 452, 904, 4859, 9718, 19436

Step-4: Factors of 38880

List of positive integer factors of 38880 that divides 38872 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38872 and 38880. The biggest common factor number is the GCF number.
So the greatest common factor 38872 and 38880 is 8.

Also check out the Least Common Multiple of 38872 and 38880