What is the Greatest Common Factor of 400 and 414?

Greatest common factor (GCF) of 400 and 414 is 2.

GCF(400,414) = 2

We will now calculate the prime factors of 400 and 414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 400 and 414.

How to find the GCF of 400 and 414?

We will first find the prime factorization of 400 and 414. After we will calculate the factors of 400 and 414 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 414

Prime factors of 414 are 2, 3, 23. Prime factorization of 414 in exponential form is:

414 = 2¹ × 3² × 23¹

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 414

List of positive integer factors of 414 that divides 400 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 400 and 414. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 414 is 2.

Also check out the Least Common Multiple of 400 and 414