What is the Greatest Common Factor of 22617 and 22624?

Greatest common factor (GCF) of 22617 and 22624 is 7.

GCF(22617,22624) = 7

We will now calculate the prime factors of 22617 and 22624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22617 and 22624.

How to find the GCF of 22617 and 22624?

We will first find the prime factorization of 22617 and 22624. After we will calculate the factors of 22617 and 22624 and find the biggest common factor number .

Step-1: Prime Factorization of 22617

Prime factors of 22617 are 3, 7, 359. Prime factorization of 22617 in exponential form is:

22617 = 3² × 7¹ × 359¹

Step-2: 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-3: Factors of 22617

List of positive integer factors of 22617 that divides 22617 without a remainder.

1, 3, 7, 9, 21, 63, 359, 1077, 2513, 3231, 7539

Step-4: Factors of 22624

List of positive integer factors of 22624 that divides 22617 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22617 and 22624. The biggest common factor number is the GCF number.
So the greatest common factor 22617 and 22624 is 7.

Also check out the Least Common Multiple of 22617 and 22624