What is the Greatest Common Factor of 16400 and 16419?

Greatest common factor (GCF) of 16400 and 16419 is 1.

GCF(16400,16419) = 1

We will now calculate the prime factors of 16400 and 16419, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16400 and 16419.

How to find the GCF of 16400 and 16419?

We will first find the prime factorization of 16400 and 16419. After we will calculate the factors of 16400 and 16419 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 16419

Prime factors of 16419 are 3, 13, 421. Prime factorization of 16419 in exponential form is:

16419 = 3¹ × 13¹ × 421¹

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 16419

List of positive integer factors of 16419 that divides 16400 without a remainder.

1, 3, 13, 39, 421, 1263, 5473

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16400 and 16419. The biggest common factor number is the GCF number.
So the greatest common factor 16400 and 16419 is 1.

Also check out the Least Common Multiple of 16400 and 16419