What is the Greatest Common Factor of 10638 and 10653?

Greatest common factor (GCF) of 10638 and 10653 is 3.

GCF(10638,10653) = 3

We will now calculate the prime factors of 10638 and 10653, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10638 and 10653.

How to find the GCF of 10638 and 10653?

We will first find the prime factorization of 10638 and 10653. After we will calculate the factors of 10638 and 10653 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10653

Prime factors of 10653 are 3, 53, 67. Prime factorization of 10653 in exponential form is:

10653 = 3¹ × 53¹ × 67¹

Step-3: Factors of 10638

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

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

Step-4: Factors of 10653

List of positive integer factors of 10653 that divides 10638 without a remainder.

1, 3, 53, 67, 159, 201, 3551

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10638 and 10653. The biggest common factor number is the GCF number.
So the greatest common factor 10638 and 10653 is 3.

Also check out the Least Common Multiple of 10638 and 10653