What is the Greatest Common Factor of 22624 and 22638?

Greatest common factor (GCF) of 22624 and 22638 is 14.

GCF(22624,22638) = 14

We will now calculate the prime factors of 22624 and 22638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22624 and 22638.

How to find the GCF of 22624 and 22638?

We will first find the prime factorization of 22624 and 22638. After we will calculate the factors of 22624 and 22638 and find the biggest common factor number .

Step-1: Prime Factorization of 22624

Prime factors of 22624 are 2, 7, 101. Prime factorization of 22624 in exponential form is:

22624 = 2⁵ × 7¹ × 101¹

Step-2: Prime Factorization of 22638

Prime factors of 22638 are 2, 3, 7, 11. Prime factorization of 22638 in exponential form is:

22638 = 2¹ × 3¹ × 7³ × 11¹

Step-3: Factors of 22624

List of positive integer factors of 22624 that divides 22624 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 101, 112, 202, 224, 404, 707, 808, 1414, 1616, 2828, 3232, 5656, 11312

Step-4: Factors of 22638

List of positive integer factors of 22638 that divides 22624 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 49, 66, 77, 98, 147, 154, 231, 294, 343, 462, 539, 686, 1029, 1078, 1617, 2058, 3234, 3773, 7546, 11319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22624 and 22638. The biggest common factor number is the GCF number.
So the greatest common factor 22624 and 22638 is 14.

Also check out the Least Common Multiple of 22624 and 22638