What is the Greatest Common Factor of 13617 and 13632?

Greatest common factor (GCF) of 13617 and 13632 is 3.

GCF(13617,13632) = 3

We will now calculate the prime factors of 13617 and 13632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13617 and 13632.

How to find the GCF of 13617 and 13632?

We will first find the prime factorization of 13617 and 13632. After we will calculate the factors of 13617 and 13632 and find the biggest common factor number .

Step-1: Prime Factorization of 13617

Prime factors of 13617 are 3, 17, 89. Prime factorization of 13617 in exponential form is:

13617 = 3² × 17¹ × 89¹

Step-2: 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-3: Factors of 13617

List of positive integer factors of 13617 that divides 13617 without a remainder.

1, 3, 9, 17, 51, 89, 153, 267, 801, 1513, 4539

Step-4: Factors of 13632

List of positive integer factors of 13632 that divides 13617 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13617 and 13632. The biggest common factor number is the GCF number.
So the greatest common factor 13617 and 13632 is 3.

Also check out the Least Common Multiple of 13617 and 13632