What is the Greatest Common Factor of 400 and 404?

Greatest common factor (GCF) of 400 and 404 is 4.

GCF(400,404) = 4

We will now calculate the prime factors of 400 and 404, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 400 and 404.

How to find the GCF of 400 and 404?

We will first find the prime factorization of 400 and 404. After we will calculate the factors of 400 and 404 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 404

Prime factors of 404 are 2, 101. Prime factorization of 404 in exponential form is:

404 = 2² × 101¹

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 404

List of positive integer factors of 404 that divides 400 without a remainder.

1, 2, 4, 101, 202

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 400 and 404. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 404 is 4.

Also check out the Least Common Multiple of 400 and 404