What is the Greatest Common Factor of 21874 and 21888?

Greatest common factor (GCF) of 21874 and 21888 is 2.

GCF(21874,21888) = 2

We will now calculate the prime factors of 21874 and 21888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21874 and 21888.

How to find the GCF of 21874 and 21888?

We will first find the prime factorization of 21874 and 21888. After we will calculate the factors of 21874 and 21888 and find the biggest common factor number .

Step-1: Prime Factorization of 21874

Prime factors of 21874 are 2, 10937. Prime factorization of 21874 in exponential form is:

21874 = 2¹ × 10937¹

Step-2: 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-3: Factors of 21874

List of positive integer factors of 21874 that divides 21874 without a remainder.

1, 2, 10937

Step-4: Factors of 21888

List of positive integer factors of 21888 that divides 21874 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21874 and 21888. The biggest common factor number is the GCF number.
So the greatest common factor 21874 and 21888 is 2.

Also check out the Least Common Multiple of 21874 and 21888