What is the Greatest Common Factor of 14400 and 14410?

Greatest common factor (GCF) of 14400 and 14410 is 10.

GCF(14400,14410) = 10

We will now calculate the prime factors of 14400 and 14410, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14400 and 14410.

How to find the GCF of 14400 and 14410?

We will first find the prime factorization of 14400 and 14410. After we will calculate the factors of 14400 and 14410 and find the biggest common factor number .

Step-1: Prime Factorization of 14400

Prime factors of 14400 are 2, 3, 5. Prime factorization of 14400 in exponential form is:

14400 = 2⁶ × 3² × 5²

Step-2: Prime Factorization of 14410

Prime factors of 14410 are 2, 5, 11, 131. Prime factorization of 14410 in exponential form is:

14410 = 2¹ × 5¹ × 11¹ × 131¹

Step-3: Factors of 14400

List of positive integer factors of 14400 that divides 14400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 400, 450, 480, 576, 600, 720, 800, 900, 960, 1200, 1440, 1600, 1800, 2400, 2880, 3600, 4800, 7200

Step-4: Factors of 14410

List of positive integer factors of 14410 that divides 14400 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 131, 262, 655, 1310, 1441, 2882, 7205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14400 and 14410. The biggest common factor number is the GCF number.
So the greatest common factor 14400 and 14410 is 10.

Also check out the Least Common Multiple of 14400 and 14410