What is the Greatest Common Factor of 21888 and 21906?

Greatest common factor (GCF) of 21888 and 21906 is 18.

GCF(21888,21906) = 18

We will now calculate the prime factors of 21888 and 21906, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21888 and 21906.

How to find the GCF of 21888 and 21906?

We will first find the prime factorization of 21888 and 21906. After we will calculate the factors of 21888 and 21906 and find the biggest common factor number .

Step-1: Prime Factorization of 21888

Prime factors of 21888 are 2, 3, 19. Prime factorization of 21888 in exponential form is:

21888 = 2⁷ × 3² × 19¹

Step-2: Prime Factorization of 21906

Prime factors of 21906 are 2, 3, 1217. Prime factorization of 21906 in exponential form is:

21906 = 2¹ × 3² × 1217¹

Step-3: Factors of 21888

List of positive integer factors of 21888 that divides 21888 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48, 57, 64, 72, 76, 96, 114, 128, 144, 152, 171, 192, 228, 288, 304, 342, 384, 456, 576, 608, 684, 912, 1152, 1216, 1368, 1824, 2432, 2736, 3648, 5472, 7296, 10944

Step-4: Factors of 21906

List of positive integer factors of 21906 that divides 21888 without a remainder.

1, 2, 3, 6, 9, 18, 1217, 2434, 3651, 7302, 10953

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21888 and 21906. The biggest common factor number is the GCF number.
So the greatest common factor 21888 and 21906 is 18.

Also check out the Least Common Multiple of 21888 and 21906