What is the Greatest Common Factor of 385 and 400?

Greatest common factor (GCF) of 385 and 400 is 5.

GCF(385,400) = 5

We will now calculate the prime factors of 385 and 400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 385 and 400.

How to find the GCF of 385 and 400?

We will first find the prime factorization of 385 and 400. After we will calculate the factors of 385 and 400 and find the biggest common factor number .

Step-1: Prime Factorization of 385

Prime factors of 385 are 5, 7, 11. Prime factorization of 385 in exponential form is:

385 = 5¹ × 7¹ × 11¹

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 385

List of positive integer factors of 385 that divides 385 without a remainder.

1, 5, 7, 11, 35, 55, 77

Step-4: Factors of 400

List of positive integer factors of 400 that divides 385 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 385 and 400. The biggest common factor number is the GCF number.
So the greatest common factor 385 and 400 is 5.

Also check out the Least Common Multiple of 385 and 400