What is the Greatest Common Factor of 400 and 409?

Greatest common factor (GCF) of 400 and 409 is 1.

GCF(400,409) = 1

We will now calculate the prime factors of 400 and 409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 400 and 409.

How to find the GCF of 400 and 409?

We will first find the prime factorization of 400 and 409. After we will calculate the factors of 400 and 409 and find the biggest common factor number .

Step-1: Prime Factorization of 400

Prime factors of 400 are 2, 5. Prime factorization of 400 in exponential form is:

400 = 2⁴ × 5²

Step-2: Prime Factorization of 409

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 409¹

Step-3: Factors of 400

List of positive integer factors of 400 that divides 400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200

Step-4: Factors of 409

List of positive integer factors of 409 that divides 400 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 400 and 409. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 409 is 1.

Also check out the Least Common Multiple of 400 and 409