What is the Greatest Common Factor of 20400 and 20416?

Greatest common factor (GCF) of 20400 and 20416 is 16.

GCF(20400,20416) = 16

We will now calculate the prime factors of 20400 and 20416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20400 and 20416.

How to find the GCF of 20400 and 20416?

We will first find the prime factorization of 20400 and 20416. After we will calculate the factors of 20400 and 20416 and find the biggest common factor number .

Step-1: Prime Factorization of 20400

Prime factors of 20400 are 2, 3, 5, 17. Prime factorization of 20400 in exponential form is:

20400 = 2⁴ × 3¹ × 5² × 17¹

Step-2: Prime Factorization of 20416

Prime factors of 20416 are 2, 11, 29. Prime factorization of 20416 in exponential form is:

20416 = 2⁶ × 11¹ × 29¹

Step-3: Factors of 20400

List of positive integer factors of 20400 that divides 20400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200

Step-4: Factors of 20416

List of positive integer factors of 20416 that divides 20400 without a remainder.

1, 2, 4, 8, 11, 16, 22, 29, 32, 44, 58, 64, 88, 116, 176, 232, 319, 352, 464, 638, 704, 928, 1276, 1856, 2552, 5104, 10208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20400 and 20416. The biggest common factor number is the GCF number.
So the greatest common factor 20400 and 20416 is 16.

Also check out the Least Common Multiple of 20400 and 20416