What is the Greatest Common Factor of 400 and 410?

Greatest common factor (GCF) of 400 and 410 is 10.

GCF(400,410) = 10

We will now calculate the prime factors of 400 and 410, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 400 and 410.

How to find the GCF of 400 and 410?

We will first find the prime factorization of 400 and 410. After we will calculate the factors of 400 and 410 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 410

Prime factors of 410 are 2, 5, 41. Prime factorization of 410 in exponential form is:

410 = 2¹ × 5¹ × 41¹

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 410

List of positive integer factors of 410 that divides 400 without a remainder.

1, 2, 5, 10, 41, 82, 205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 400 and 410. The biggest common factor number is the GCF number.
So the greatest common factor 400 and 410 is 10.

Also check out the Least Common Multiple of 400 and 410