What is the Greatest Common Factor of 13824 and 13828?

Greatest common factor (GCF) of 13824 and 13828 is 4.

GCF(13824,13828) = 4

We will now calculate the prime factors of 13824 and 13828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13824 and 13828.

How to find the GCF of 13824 and 13828?

We will first find the prime factorization of 13824 and 13828. After we will calculate the factors of 13824 and 13828 and find the biggest common factor number .

Step-1: Prime Factorization of 13824

Prime factors of 13824 are 2, 3. Prime factorization of 13824 in exponential form is:

13824 = 2⁹ × 3³

Step-2: Prime Factorization of 13828

Prime factors of 13828 are 2, 3457. Prime factorization of 13828 in exponential form is:

13828 = 2² × 3457¹

Step-3: Factors of 13824

List of positive integer factors of 13824 that divides 13824 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912

Step-4: Factors of 13828

List of positive integer factors of 13828 that divides 13824 without a remainder.

1, 2, 4, 3457, 6914

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13824 and 13828. The biggest common factor number is the GCF number.
So the greatest common factor 13824 and 13828 is 4.

Also check out the Least Common Multiple of 13824 and 13828