What is the Greatest Common Factor of 13425 and 13440?

Greatest common factor (GCF) of 13425 and 13440 is 15.

GCF(13425,13440) = 15

We will now calculate the prime factors of 13425 and 13440, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13425 and 13440.

How to find the GCF of 13425 and 13440?

We will first find the prime factorization of 13425 and 13440. After we will calculate the factors of 13425 and 13440 and find the biggest common factor number .

Step-1: Prime Factorization of 13425

Prime factors of 13425 are 3, 5, 179. Prime factorization of 13425 in exponential form is:

13425 = 3¹ × 5² × 179¹

Step-2: 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-3: Factors of 13425

List of positive integer factors of 13425 that divides 13425 without a remainder.

1, 3, 5, 15, 25, 75, 179, 537, 895, 2685, 4475

Step-4: Factors of 13440

List of positive integer factors of 13440 that divides 13425 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13425 and 13440. The biggest common factor number is the GCF number.
So the greatest common factor 13425 and 13440 is 15.

Also check out the Least Common Multiple of 13425 and 13440