What is the Greatest Common Factor of 13814 and 13824?

Greatest common factor (GCF) of 13814 and 13824 is 2.

GCF(13814,13824) = 2

We will now calculate the prime factors of 13814 and 13824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13814 and 13824.

How to find the GCF of 13814 and 13824?

We will first find the prime factorization of 13814 and 13824. After we will calculate the factors of 13814 and 13824 and find the biggest common factor number .

Step-1: Prime Factorization of 13814

Prime factors of 13814 are 2, 6907. Prime factorization of 13814 in exponential form is:

13814 = 2¹ × 6907¹

Step-2: Prime Factorization of 13824

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

13824 = 2⁹ × 3³

Step-3: Factors of 13814

List of positive integer factors of 13814 that divides 13814 without a remainder.

1, 2, 6907

Step-4: Factors of 13824

List of positive integer factors of 13824 that divides 13814 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13814 and 13824. The biggest common factor number is the GCF number.
So the greatest common factor 13814 and 13824 is 2.

Also check out the Least Common Multiple of 13814 and 13824