What is the Greatest Common Factor of 13638 and 13652?

Greatest common factor (GCF) of 13638 and 13652 is 2.

GCF(13638,13652) = 2

We will now calculate the prime factors of 13638 and 13652, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13638 and 13652.

How to find the GCF of 13638 and 13652?

We will first find the prime factorization of 13638 and 13652. After we will calculate the factors of 13638 and 13652 and find the biggest common factor number .

Step-1: Prime Factorization of 13638

Prime factors of 13638 are 2, 3, 2273. Prime factorization of 13638 in exponential form is:

13638 = 2¹ × 3¹ × 2273¹

Step-2: Prime Factorization of 13652

Prime factors of 13652 are 2, 3413. Prime factorization of 13652 in exponential form is:

13652 = 2² × 3413¹

Step-3: Factors of 13638

List of positive integer factors of 13638 that divides 13638 without a remainder.

1, 2, 3, 6, 2273, 4546, 6819

Step-4: Factors of 13652

List of positive integer factors of 13652 that divides 13638 without a remainder.

1, 2, 4, 3413, 6826

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13638 and 13652. The biggest common factor number is the GCF number.
So the greatest common factor 13638 and 13652 is 2.

Also check out the Least Common Multiple of 13638 and 13652