What is the Greatest Common Factor of 405 and 417?

Greatest common factor (GCF) of 405 and 417 is 3.

GCF(405,417) = 3

We will now calculate the prime factors of 405 and 417, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 405 and 417.

How to find the GCF of 405 and 417?

We will first find the prime factorization of 405 and 417. After we will calculate the factors of 405 and 417 and find the biggest common factor number .

Step-1: Prime Factorization of 405

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

405 = 3⁴ × 5¹

Step-2: Prime Factorization of 417

Prime factors of 417 are 3, 139. Prime factorization of 417 in exponential form is:

417 = 3¹ × 139¹

Step-3: Factors of 405

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

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

Step-4: Factors of 417

List of positive integer factors of 417 that divides 405 without a remainder.

1, 3, 139

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 405 and 417. The biggest common factor number is the GCF number.
So the greatest common factor 405 and 417 is 3.

Also check out the Least Common Multiple of 405 and 417