What is the Greatest Common Factor of 390 and 405?

Greatest common factor (GCF) of 390 and 405 is 15.

GCF(390,405) = 15

We will now calculate the prime factors of 390 and 405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 390 and 405.

How to find the GCF of 390 and 405?

We will first find the prime factorization of 390 and 405. After we will calculate the factors of 390 and 405 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 405

Prime factors of 405 are 3, 5. Prime factorization of 405 in exponential form is:

405 = 3⁴ × 5¹

Step-3: Factors of 390

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

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

Step-4: Factors of 405

List of positive integer factors of 405 that divides 390 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 390 and 405. The biggest common factor number is the GCF number.
So the greatest common factor 390 and 405 is 15.

Also check out the Least Common Multiple of 390 and 405