What is the Greatest Common Factor of 13653 and 13662?

Greatest common factor (GCF) of 13653 and 13662 is 9.

GCF(13653,13662) = 9

We will now calculate the prime factors of 13653 and 13662, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13653 and 13662.

How to find the GCF of 13653 and 13662?

We will first find the prime factorization of 13653 and 13662. After we will calculate the factors of 13653 and 13662 and find the biggest common factor number .

Step-1: Prime Factorization of 13653

Prime factors of 13653 are 3, 37, 41. Prime factorization of 13653 in exponential form is:

13653 = 3² × 37¹ × 41¹

Step-2: Prime Factorization of 13662

Prime factors of 13662 are 2, 3, 11, 23. Prime factorization of 13662 in exponential form is:

13662 = 2¹ × 3³ × 11¹ × 23¹

Step-3: Factors of 13653

List of positive integer factors of 13653 that divides 13653 without a remainder.

1, 3, 9, 37, 41, 111, 123, 333, 369, 1517, 4551

Step-4: Factors of 13662

List of positive integer factors of 13662 that divides 13653 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 23, 27, 33, 46, 54, 66, 69, 99, 138, 198, 207, 253, 297, 414, 506, 594, 621, 759, 1242, 1518, 2277, 4554, 6831

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13653 and 13662. The biggest common factor number is the GCF number.
So the greatest common factor 13653 and 13662 is 9.

Also check out the Least Common Multiple of 13653 and 13662