What is the Greatest Common Factor of 21888 and 21905?

Greatest common factor (GCF) of 21888 and 21905 is 1.

GCF(21888,21905) = 1

We will now calculate the prime factors of 21888 and 21905, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21888 and 21905.

How to find the GCF of 21888 and 21905?

We will first find the prime factorization of 21888 and 21905. After we will calculate the factors of 21888 and 21905 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 21905

Prime factors of 21905 are 5, 13, 337. Prime factorization of 21905 in exponential form is:

21905 = 5¹ × 13¹ × 337¹

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 21905

List of positive integer factors of 21905 that divides 21888 without a remainder.

1, 5, 13, 65, 337, 1685, 4381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21888 and 21905. The biggest common factor number is the GCF number.
So the greatest common factor 21888 and 21905 is 1.

Also check out the Least Common Multiple of 21888 and 21905