What is the Greatest Common Factor of 16400 and 16409?

Greatest common factor (GCF) of 16400 and 16409 is 1.

GCF(16400,16409) = 1

We will now calculate the prime factors of 16400 and 16409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16400 and 16409.

How to find the GCF of 16400 and 16409?

We will first find the prime factorization of 16400 and 16409. After we will calculate the factors of 16400 and 16409 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 16409

Prime factors of 16409 are 61, 269. Prime factorization of 16409 in exponential form is:

16409 = 61¹ × 269¹

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 16409

List of positive integer factors of 16409 that divides 16400 without a remainder.

1, 61, 269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16400 and 16409. The biggest common factor number is the GCF number.
So the greatest common factor 16400 and 16409 is 1.

Also check out the Least Common Multiple of 16400 and 16409