What is the Greatest Common Factor of 10 and 400?

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

GCF(10,400) = 10

We will now calculate the prime factors of 10 and 400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10 and 400.

How to find the GCF of 10 and 400?

We will first find the prime factorization of 10 and 400. After we will calculate the factors of 10 and 400 and find the biggest common factor number .

Step-1: Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 2¹ × 5¹

Step-2: Prime Factorization of 400

Prime factors of 400 are 2, 5. Prime factorization of 400 in exponential form is:

400 = 2⁴ × 5²

Step-3: Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5

Step-4: Factors of 400

List of positive integer factors of 400 that divides 10 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200

Final Step: Biggest Common Factor Number

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

Also check out the Least Common Multiple of 10 and 400