What is the Greatest Common Factor of 13824 and 13830?

Greatest common factor (GCF) of 13824 and 13830 is 6.

GCF(13824,13830) = 6

We will now calculate the prime factors of 13824 and 13830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13824 and 13830.

How to find the GCF of 13824 and 13830?

We will first find the prime factorization of 13824 and 13830. After we will calculate the factors of 13824 and 13830 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 13830

Prime factors of 13830 are 2, 3, 5, 461. Prime factorization of 13830 in exponential form is:

13830 = 2¹ × 3¹ × 5¹ × 461¹

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 13830

List of positive integer factors of 13830 that divides 13824 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 461, 922, 1383, 2305, 2766, 4610, 6915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13824 and 13830. The biggest common factor number is the GCF number.
So the greatest common factor 13824 and 13830 is 6.

Also check out the Least Common Multiple of 13824 and 13830