What is the Greatest Common Factor of 21906 and 21924?

Greatest common factor (GCF) of 21906 and 21924 is 18.

GCF(21906,21924) = 18

We will now calculate the prime factors of 21906 and 21924, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21906 and 21924.

How to find the GCF of 21906 and 21924?

We will first find the prime factorization of 21906 and 21924. After we will calculate the factors of 21906 and 21924 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21924

Prime factors of 21924 are 2, 3, 7, 29. Prime factorization of 21924 in exponential form is:

21924 = 2² × 3³ × 7¹ × 29¹

Step-3: Factors of 21906

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

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

Step-4: Factors of 21924

List of positive integer factors of 21924 that divides 21906 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 29, 36, 42, 54, 58, 63, 84, 87, 108, 116, 126, 174, 189, 203, 252, 261, 348, 378, 406, 522, 609, 756, 783, 812, 1044, 1218, 1566, 1827, 2436, 3132, 3654, 5481, 7308, 10962

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21906 and 21924. The biggest common factor number is the GCF number.
So the greatest common factor 21906 and 21924 is 18.

Also check out the Least Common Multiple of 21906 and 21924