What is the Greatest Common Factor of 396 and 407?

Greatest common factor (GCF) of 396 and 407 is 11.

GCF(396,407) = 11

We will now calculate the prime factors of 396 and 407, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 396 and 407.

How to find the GCF of 396 and 407?

We will first find the prime factorization of 396 and 407. After we will calculate the factors of 396 and 407 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 407

Prime factors of 407 are 11, 37. Prime factorization of 407 in exponential form is:

407 = 11¹ × 37¹

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 407

List of positive integer factors of 407 that divides 396 without a remainder.

1, 11, 37

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 396 and 407. The biggest common factor number is the GCF number.
So the greatest common factor 396 and 407 is 11.

Also check out the Least Common Multiple of 396 and 407