What is the Greatest Common Factor of 16400 and 16416?

Greatest common factor (GCF) of 16400 and 16416 is 16.

GCF(16400,16416) = 16

We will now calculate the prime factors of 16400 and 16416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16400 and 16416.

How to find the GCF of 16400 and 16416?

We will first find the prime factorization of 16400 and 16416. After we will calculate the factors of 16400 and 16416 and find the biggest common factor number .

Step-1: Prime Factorization of 16400

Prime factors of 16400 are 2, 5, 41. Prime factorization of 16400 in exponential form is:

16400 = 2⁴ × 5² × 41¹

Step-2: Prime Factorization of 16416

Prime factors of 16416 are 2, 3, 19. Prime factorization of 16416 in exponential form is:

16416 = 2⁵ × 3³ × 19¹

Step-3: Factors of 16400

List of positive integer factors of 16400 that divides 16400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 164, 200, 205, 328, 400, 410, 656, 820, 1025, 1640, 2050, 3280, 4100, 8200

Step-4: Factors of 16416

List of positive integer factors of 16416 that divides 16400 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 72, 76, 96, 108, 114, 144, 152, 171, 216, 228, 288, 304, 342, 432, 456, 513, 608, 684, 864, 912, 1026, 1368, 1824, 2052, 2736, 4104, 5472, 8208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16400 and 16416. The biggest common factor number is the GCF number.
So the greatest common factor 16400 and 16416 is 16.

Also check out the Least Common Multiple of 16400 and 16416