What is the Greatest Common Factor of 384 and 390?

Greatest common factor (GCF) of 384 and 390 is 6.

GCF(384,390) = 6

We will now calculate the prime factors of 384 and 390, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 384 and 390.

How to find the GCF of 384 and 390?

We will first find the prime factorization of 384 and 390. After we will calculate the factors of 384 and 390 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 390

Prime factors of 390 are 2, 3, 5, 13. Prime factorization of 390 in exponential form is:

390 = 2¹ × 3¹ × 5¹ × 13¹

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 390

List of positive integer factors of 390 that divides 384 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 384 and 390. The biggest common factor number is the GCF number.
So the greatest common factor 384 and 390 is 6.

Also check out the Least Common Multiple of 384 and 390