What is the Greatest Common Factor of 408 and 417?

Greatest common factor (GCF) of 408 and 417 is 3.

GCF(408,417) = 3

We will now calculate the prime factors of 408 and 417, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 408 and 417.

How to find the GCF of 408 and 417?

We will first find the prime factorization of 408 and 417. After we will calculate the factors of 408 and 417 and find the biggest common factor number .

Step-1: Prime Factorization of 408

Prime factors of 408 are 2, 3, 17. Prime factorization of 408 in exponential form is:

408 = 2³ × 3¹ × 17¹

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 408

List of positive integer factors of 408 that divides 408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204

Step-4: Factors of 417

List of positive integer factors of 417 that divides 408 without a remainder.

1, 3, 139

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 408 and 417. The biggest common factor number is the GCF number.
So the greatest common factor 408 and 417 is 3.

Also check out the Least Common Multiple of 408 and 417