What is the Greatest Common Factor of 21609 and 21624?

Greatest common factor (GCF) of 21609 and 21624 is 3.

GCF(21609,21624) = 3

We will now calculate the prime factors of 21609 and 21624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21609 and 21624.

How to find the GCF of 21609 and 21624?

We will first find the prime factorization of 21609 and 21624. After we will calculate the factors of 21609 and 21624 and find the biggest common factor number .

Step-1: Prime Factorization of 21609

Prime factors of 21609 are 3, 7. Prime factorization of 21609 in exponential form is:

21609 = 3² × 7⁴

Step-2: Prime Factorization of 21624

Prime factors of 21624 are 2, 3, 17, 53. Prime factorization of 21624 in exponential form is:

21624 = 2³ × 3¹ × 17¹ × 53¹

Step-3: Factors of 21609

List of positive integer factors of 21609 that divides 21609 without a remainder.

1, 3, 7, 9, 21, 49, 63, 147, 343, 441, 1029, 2401, 3087, 7203

Step-4: Factors of 21624

List of positive integer factors of 21624 that divides 21609 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 53, 68, 102, 106, 136, 159, 204, 212, 318, 408, 424, 636, 901, 1272, 1802, 2703, 3604, 5406, 7208, 10812

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21609 and 21624. The biggest common factor number is the GCF number.
So the greatest common factor 21609 and 21624 is 3.

Also check out the Least Common Multiple of 21609 and 21624