What is the Greatest Common Factor of 400 and 415?

Greatest common factor (GCF) of 400 and 415 is 5.

GCF(400,415) = 5

We will now calculate the prime factors of 400 and 415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 400 and 415.

How to find the GCF of 400 and 415?

We will first find the prime factorization of 400 and 415. After we will calculate the factors of 400 and 415 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 415

Prime factors of 415 are 5, 83. Prime factorization of 415 in exponential form is:

415 = 5¹ × 83¹

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 415

List of positive integer factors of 415 that divides 400 without a remainder.

1, 5, 83

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 400 and 415. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 415 is 5.

Also check out the Least Common Multiple of 400 and 415