What is the Greatest Common Factor of 398 and 408?

Greatest common factor (GCF) of 398 and 408 is 2.

GCF(398,408) = 2

We will now calculate the prime factors of 398 and 408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 398 and 408.

How to find the GCF of 398 and 408?

We will first find the prime factorization of 398 and 408. After we will calculate the factors of 398 and 408 and find the biggest common factor number .

Step-1: Prime Factorization of 398

Prime factors of 398 are 2, 199. Prime factorization of 398 in exponential form is:

398 = 2¹ × 199¹

Step-2: 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-3: Factors of 398

List of positive integer factors of 398 that divides 398 without a remainder.

1, 2, 199

Step-4: Factors of 408

List of positive integer factors of 408 that divides 398 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 398 and 408. The biggest common factor number is the GCF number.
So the greatest common factor 398 and 408 is 2.

Also check out the Least Common Multiple of 398 and 408