What is the Greatest Common Factor of 22385 and 22400?

Greatest common factor (GCF) of 22385 and 22400 is 5.

GCF(22385,22400) = 5

We will now calculate the prime factors of 22385 and 22400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22385 and 22400.

How to find the GCF of 22385 and 22400?

We will first find the prime factorization of 22385 and 22400. After we will calculate the factors of 22385 and 22400 and find the biggest common factor number .

Step-1: Prime Factorization of 22385

Prime factors of 22385 are 5, 11, 37. Prime factorization of 22385 in exponential form is:

22385 = 5¹ × 11² × 37¹

Step-2: Prime Factorization of 22400

Prime factors of 22400 are 2, 5, 7. Prime factorization of 22400 in exponential form is:

22400 = 2⁷ × 5² × 7¹

Step-3: Factors of 22385

List of positive integer factors of 22385 that divides 22385 without a remainder.

1, 5, 11, 37, 55, 121, 185, 407, 605, 2035, 4477

Step-4: Factors of 22400

List of positive integer factors of 22400 that divides 22385 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 128, 140, 160, 175, 200, 224, 280, 320, 350, 400, 448, 560, 640, 700, 800, 896, 1120, 1400, 1600, 2240, 2800, 3200, 4480, 5600, 11200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22385 and 22400. The biggest common factor number is the GCF number.
So the greatest common factor 22385 and 22400 is 5.

Also check out the Least Common Multiple of 22385 and 22400