What is the Greatest Common Factor of 10614 and 10623?

Greatest common factor (GCF) of 10614 and 10623 is 3.

GCF(10614,10623) = 3

We will now calculate the prime factors of 10614 and 10623, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10614 and 10623.

How to find the GCF of 10614 and 10623?

We will first find the prime factorization of 10614 and 10623. After we will calculate the factors of 10614 and 10623 and find the biggest common factor number .

Step-1: Prime Factorization of 10614

Prime factors of 10614 are 2, 3, 29, 61. Prime factorization of 10614 in exponential form is:

10614 = 2¹ × 3¹ × 29¹ × 61¹

Step-2: Prime Factorization of 10623

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

10623 = 3¹ × 3541¹

Step-3: Factors of 10614

List of positive integer factors of 10614 that divides 10614 without a remainder.

1, 2, 3, 6, 29, 58, 61, 87, 122, 174, 183, 366, 1769, 3538, 5307

Step-4: Factors of 10623

List of positive integer factors of 10623 that divides 10614 without a remainder.

1, 3, 3541

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10614 and 10623. The biggest common factor number is the GCF number.
So the greatest common factor 10614 and 10623 is 3.

Also check out the Least Common Multiple of 10614 and 10623