What is the Greatest Common Factor of 22386 and 22400?

Greatest common factor (GCF) of 22386 and 22400 is 14.

GCF(22386,22400) = 14

We will now calculate the prime factors of 22386 and 22400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22386 and 22400.

How to find the GCF of 22386 and 22400?

We will first find the prime factorization of 22386 and 22400. After we will calculate the factors of 22386 and 22400 and find the biggest common factor number .

Step-1: Prime Factorization of 22386

Prime factors of 22386 are 2, 3, 7, 13, 41. Prime factorization of 22386 in exponential form is:

22386 = 2¹ × 3¹ × 7¹ × 13¹ × 41¹

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 22386

List of positive integer factors of 22386 that divides 22386 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 41, 42, 78, 82, 91, 123, 182, 246, 273, 287, 533, 546, 574, 861, 1066, 1599, 1722, 3198, 3731, 7462, 11193

Step-4: Factors of 22400

List of positive integer factors of 22400 that divides 22386 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 22386 and 22400. The biggest common factor number is the GCF number.
So the greatest common factor 22386 and 22400 is 14.

Also check out the Least Common Multiple of 22386 and 22400