What is the Greatest Common Factor of 13632 and 13644?

Greatest common factor (GCF) of 13632 and 13644 is 12.

GCF(13632,13644) = 12

We will now calculate the prime factors of 13632 and 13644, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13632 and 13644.

How to find the GCF of 13632 and 13644?

We will first find the prime factorization of 13632 and 13644. After we will calculate the factors of 13632 and 13644 and find the biggest common factor number .

Step-1: Prime Factorization of 13632

Prime factors of 13632 are 2, 3, 71. Prime factorization of 13632 in exponential form is:

13632 = 2⁶ × 3¹ × 71¹

Step-2: Prime Factorization of 13644

Prime factors of 13644 are 2, 3, 379. Prime factorization of 13644 in exponential form is:

13644 = 2² × 3² × 379¹

Step-3: Factors of 13632

List of positive integer factors of 13632 that divides 13632 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 71, 96, 142, 192, 213, 284, 426, 568, 852, 1136, 1704, 2272, 3408, 4544, 6816

Step-4: Factors of 13644

List of positive integer factors of 13644 that divides 13632 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 379, 758, 1137, 1516, 2274, 3411, 4548, 6822

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13632 and 13644. The biggest common factor number is the GCF number.
So the greatest common factor 13632 and 13644 is 12.

Also check out the Least Common Multiple of 13632 and 13644