What is the Greatest Common Factor of 380 and 400?

Greatest common factor (GCF) of 380 and 400 is 20.

GCF(380,400) = 20

We will now calculate the prime factors of 380 and 400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 380 and 400.

How to find the GCF of 380 and 400?

We will first find the prime factorization of 380 and 400. After we will calculate the factors of 380 and 400 and find the biggest common factor number .

Step-1: Prime Factorization of 380

Prime factors of 380 are 2, 5, 19. Prime factorization of 380 in exponential form is:

380 = 2² × 5¹ × 19¹

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 380

List of positive integer factors of 380 that divides 380 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190

Step-4: Factors of 400

List of positive integer factors of 400 that divides 380 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 380 and 400. The biggest common factor number is the GCF number.
So the greatest common factor 380 and 400 is 20.

Also check out the Least Common Multiple of 380 and 400