What is the Greatest Common Factor of 13440 and 13460?

Greatest common factor (GCF) of 13440 and 13460 is 20.

GCF(13440,13460) = 20

We will now calculate the prime factors of 13440 and 13460, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13440 and 13460.

How to find the GCF of 13440 and 13460?

We will first find the prime factorization of 13440 and 13460. After we will calculate the factors of 13440 and 13460 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 13460

Prime factors of 13460 are 2, 5, 673. Prime factorization of 13460 in exponential form is:

13460 = 2² × 5¹ × 673¹

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 13460

List of positive integer factors of 13460 that divides 13440 without a remainder.

1, 2, 4, 5, 10, 20, 673, 1346, 2692, 3365, 6730

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13440 and 13460. The biggest common factor number is the GCF number.
So the greatest common factor 13440 and 13460 is 20.

Also check out the Least Common Multiple of 13440 and 13460