What is the Greatest Common Factor of 400 and 408?

Greatest common factor (GCF) of 400 and 408 is 8.

GCF(400,408) = 8

We will now calculate the prime factors of 400 and 408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 400 and 408.

How to find the GCF of 400 and 408?

We will first find the prime factorization of 400 and 408. After we will calculate the factors of 400 and 408 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 408

Prime factors of 408 are 2, 3, 17. Prime factorization of 408 in exponential form is:

408 = 2³ × 3¹ × 17¹

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 408

List of positive integer factors of 408 that divides 400 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 400 and 408. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 408 is 8.

Also check out the Least Common Multiple of 400 and 408