What is the Greatest Common Factor of 13632 and 13648?

Greatest common factor (GCF) of 13632 and 13648 is 16.

GCF(13632,13648) = 16

We will now calculate the prime factors of 13632 and 13648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13632 and 13648.

How to find the GCF of 13632 and 13648?

We will first find the prime factorization of 13632 and 13648. After we will calculate the factors of 13632 and 13648 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 13648

Prime factors of 13648 are 2, 853. Prime factorization of 13648 in exponential form is:

13648 = 2⁴ × 853¹

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 13648

List of positive integer factors of 13648 that divides 13632 without a remainder.

1, 2, 4, 8, 16, 853, 1706, 3412, 6824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13632 and 13648. The biggest common factor number is the GCF number.
So the greatest common factor 13632 and 13648 is 16.

Also check out the Least Common Multiple of 13632 and 13648