What is the Greatest Common Factor of 10624 and 10638?

Greatest common factor (GCF) of 10624 and 10638 is 2.

GCF(10624,10638) = 2

We will now calculate the prime factors of 10624 and 10638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10624 and 10638.

How to find the GCF of 10624 and 10638?

We will first find the prime factorization of 10624 and 10638. After we will calculate the factors of 10624 and 10638 and find the biggest common factor number .

Step-1: Prime Factorization of 10624

Prime factors of 10624 are 2, 83. Prime factorization of 10624 in exponential form is:

10624 = 2⁷ × 83¹

Step-2: Prime Factorization of 10638

Prime factors of 10638 are 2, 3, 197. Prime factorization of 10638 in exponential form is:

10638 = 2¹ × 3³ × 197¹

Step-3: Factors of 10624

List of positive integer factors of 10624 that divides 10624 without a remainder.

1, 2, 4, 8, 16, 32, 64, 83, 128, 166, 332, 664, 1328, 2656, 5312

Step-4: Factors of 10638

List of positive integer factors of 10638 that divides 10624 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 197, 394, 591, 1182, 1773, 3546, 5319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10624 and 10638. The biggest common factor number is the GCF number.
So the greatest common factor 10624 and 10638 is 2.

Also check out the Least Common Multiple of 10624 and 10638