Is 396 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 396, the answer is: No, 396 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 396) is as follows: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.

For 396 to be a prime number, it would have been required that 396 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

396 is a multiple of 1
396 is a multiple of 2
396 is a multiple of 3
396 is a multiple of 4
396 is a multiple of 6
396 is a multiple of 9
396 is a multiple of 11
396 is a multiple of 12
396 is a multiple of 18
396 is a multiple of 22
396 is a multiple of 33
396 is a multiple of 36
396 is a multiple of 44
396 is a multiple of 66
396 is a multiple of 99
396 is a multiple of 132
396 is a multiple of 198

For 396 to be a prime number, it would have been required that 396 has only two divisors, i.e., itself and 1.

Is 396 a deficient number?

No, 396 is not a deficient number: to be deficient, 396 should have been such that 396 is larger than the sum of its proper divisors, i.e., the divisors of 396 without 396 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 11 + 12 + 18 + 22 + 33 + 36 + 44 + 66 + 99 + 132 + 198 = 696).

In fact, 396 is an abundant number; 396 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 11 + 12 + 18 + 22 + 33 + 36 + 44 + 66 + 99 + 132 + 198 = 696). The smallest abundant number is 12.

Parity of 396

396 is an even number, because it is evenly divisible by 2: 396 / 2 = 198.

Find out more:

What is an even number?

Is 396 a perfect square number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 396 is about 19.900.

Thus, the square root of 396 is not an integer, and therefore 396 is not a square number.

What is the square number of 396?

The square of a number (here 396) is the result of the product of this number (396) by itself (i.e., 396 × 396); the square of 396 is sometimes called "raising 396 to the power 2", or "396 squared".

The square of 396 is 156 816 because 396 × 396 = 396² = 156 816.

As a consequence, 396 is the square root of 156 816.

Number of digits of 396

396 is a number with 3 digits.

What are the multiples of 396?

The multiples of 396 are all integers evenly divisible by 396, that is all numbers such that the remainder of the division by 396 is zero. There are infinitely many multiples of 396. The smallest multiples of 396 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 396 too, since 0 × 396 = 0
396: indeed, 396 is a multiple of itself, since 396 is evenly divisible by 396 (we have 396 / 396 = 1, so the remainder of this division is indeed zero)
792: indeed, 792 = 396 × 2
1 188: indeed, 1 188 = 396 × 3
1 584: indeed, 1 584 = 396 × 4
1 980: indeed, 1 980 = 396 × 5
etc.

How to determine whether an integer is a prime number?

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 396). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 19.900). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

Numbers near 396

Preceding numbers: …394, 395
Following numbers: 397, 398…

Nearest numbers from 396

Preceding prime number: 389
Following prime number: 397