What is the Greatest Common Factor of 384 and 400?

Greatest common factor (GCF) of 384 and 400 is 16.

GCF(384,400) = 16

We will now calculate the prime factors of 384 and 400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 384 and 400.

How to find the GCF of 384 and 400?

We will first find the prime factorization of 384 and 400. After we will calculate the factors of 384 and 400 and find the biggest common factor number .

Step-1: Prime Factorization of 384

Prime factors of 384 are 2, 3. Prime factorization of 384 in exponential form is:

384 = 2⁷ × 3¹

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 384

List of positive integer factors of 384 that divides 384 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192

Step-4: Factors of 400

List of positive integer factors of 400 that divides 384 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 384 and 400. The biggest common factor number is the GCF number.
So the greatest common factor 384 and 400 is 16.

Also check out the Least Common Multiple of 384 and 400