What is the Greatest Common Factor of 21624 and 21638?

Greatest common factor (GCF) of 21624 and 21638 is 2.

GCF(21624,21638) = 2

We will now calculate the prime factors of 21624 and 21638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21624 and 21638.

How to find the GCF of 21624 and 21638?

We will first find the prime factorization of 21624 and 21638. After we will calculate the factors of 21624 and 21638 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 21638

Prime factors of 21638 are 2, 31, 349. Prime factorization of 21638 in exponential form is:

21638 = 2¹ × 31¹ × 349¹

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 21638

List of positive integer factors of 21638 that divides 21624 without a remainder.

1, 2, 31, 62, 349, 698, 10819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21624 and 21638. The biggest common factor number is the GCF number.
So the greatest common factor 21624 and 21638 is 2.

Also check out the Least Common Multiple of 21624 and 21638