What is the Greatest Common Factor of 396 and 408?

Greatest common factor (GCF) of 396 and 408 is 12.

GCF(396,408) = 12

We will now calculate the prime factors of 396 and 408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 396 and 408.

How to find the GCF of 396 and 408?

We will first find the prime factorization of 396 and 408. After we will calculate the factors of 396 and 408 and find the biggest common factor number .

Step-1: Prime Factorization of 396

Prime factors of 396 are 2, 3, 11. Prime factorization of 396 in exponential form is:

396 = 2² × 3² × 11¹

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 396

List of positive integer factors of 396 that divides 396 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198

Step-4: Factors of 408

List of positive integer factors of 408 that divides 396 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 396 and 408. The biggest common factor number is the GCF number.
So the greatest common factor 396 and 408 is 12.

Also check out the Least Common Multiple of 396 and 408