What is the Greatest Common Factor of 10623 and 10638?

Greatest common factor (GCF) of 10623 and 10638 is 3.

GCF(10623,10638) = 3

We will now calculate the prime factors of 10623 and 10638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10623 and 10638.

How to find the GCF of 10623 and 10638?

We will first find the prime factorization of 10623 and 10638. After we will calculate the factors of 10623 and 10638 and find the biggest common factor number .

Step-1: Prime Factorization of 10623

Prime factors of 10623 are 3, 3541. Prime factorization of 10623 in exponential form is:

10623 = 3¹ × 3541¹

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 10623

List of positive integer factors of 10623 that divides 10623 without a remainder.

1, 3, 3541

Step-4: Factors of 10638

List of positive integer factors of 10638 that divides 10623 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 10623 and 10638. The biggest common factor number is the GCF number.
So the greatest common factor 10623 and 10638 is 3.

Also check out the Least Common Multiple of 10623 and 10638