What is the Greatest Common Factor of 21624 and 21630?

Greatest common factor (GCF) of 21624 and 21630 is 6.

GCF(21624,21630) = 6

We will now calculate the prime factors of 21624 and 21630, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21624 and 21630.

How to find the GCF of 21624 and 21630?

We will first find the prime factorization of 21624 and 21630. After we will calculate the factors of 21624 and 21630 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21630

Prime factors of 21630 are 2, 3, 5, 7, 103. Prime factorization of 21630 in exponential form is:

21630 = 2¹ × 3¹ × 5¹ × 7¹ × 103¹

Step-3: Factors of 21624

List of positive integer factors of 21624 that divides 21624 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

Step-4: Factors of 21630

List of positive integer factors of 21630 that divides 21624 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 103, 105, 206, 210, 309, 515, 618, 721, 1030, 1442, 1545, 2163, 3090, 3605, 4326, 7210, 10815

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21624 and 21630. The biggest common factor number is the GCF number.
So the greatest common factor 21624 and 21630 is 6.

Also check out the Least Common Multiple of 21624 and 21630