What is the Greatest Common Factor of 13440 and 13456?

Greatest common factor (GCF) of 13440 and 13456 is 16.

GCF(13440,13456) = 16

We will now calculate the prime factors of 13440 and 13456, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13440 and 13456.

How to find the GCF of 13440 and 13456?

We will first find the prime factorization of 13440 and 13456. After we will calculate the factors of 13440 and 13456 and find the biggest common factor number .

Step-1: Prime Factorization of 13440

Prime factors of 13440 are 2, 3, 5, 7. Prime factorization of 13440 in exponential form is:

13440 = 2⁷ × 3¹ × 5¹ × 7¹

Step-2: Prime Factorization of 13456

Prime factors of 13456 are 2, 29. Prime factorization of 13456 in exponential form is:

13456 = 2⁴ × 29²

Step-3: Factors of 13440

List of positive integer factors of 13440 that divides 13440 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 384, 420, 448, 480, 560, 640, 672, 840, 896, 960, 1120, 1344, 1680, 1920, 2240, 2688, 3360, 4480, 6720

Step-4: Factors of 13456

List of positive integer factors of 13456 that divides 13440 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 232, 464, 841, 1682, 3364, 6728

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13440 and 13456. The biggest common factor number is the GCF number.
So the greatest common factor 13440 and 13456 is 16.

Also check out the Least Common Multiple of 13440 and 13456