What is the Greatest Common Factor of 22400 and 22416?

Greatest common factor (GCF) of 22400 and 22416 is 16.

GCF(22400,22416) = 16

We will now calculate the prime factors of 22400 and 22416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22400 and 22416.

How to find the GCF of 22400 and 22416?

We will first find the prime factorization of 22400 and 22416. After we will calculate the factors of 22400 and 22416 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 22416

Prime factors of 22416 are 2, 3, 467. Prime factorization of 22416 in exponential form is:

22416 = 2⁴ × 3¹ × 467¹

Step-3: Factors of 22400

List of positive integer factors of 22400 that divides 22400 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

Step-4: Factors of 22416

List of positive integer factors of 22416 that divides 22400 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 467, 934, 1401, 1868, 2802, 3736, 5604, 7472, 11208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22400 and 22416. The biggest common factor number is the GCF number.
So the greatest common factor 22400 and 22416 is 16.

Also check out the Least Common Multiple of 22400 and 22416