Is 996 a prime number?

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

For 996, the answer is: No, 996 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 996) is as follows: 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996.

For 996 to be a prime number, it would have been required that 996 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

996 is a multiple of 1
996 is a multiple of 2
996 is a multiple of 3
996 is a multiple of 4
996 is a multiple of 6
996 is a multiple of 12
996 is a multiple of 83
996 is a multiple of 166
996 is a multiple of 249
996 is a multiple of 332
996 is a multiple of 498

For 996 to be a prime number, it would have been required that 996 has only two divisors, i.e., itself and 1.

Is 996 a deficient number?

No, 996 is not a deficient number: to be deficient, 996 should have been such that 996 is larger than the sum of its proper divisors, i.e., the divisors of 996 without 996 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 83 + 166 + 249 + 332 + 498 = 1 356).

In fact, 996 is an abundant number; 996 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 83 + 166 + 249 + 332 + 498 = 1 356). The smallest abundant number is 12.

Parity of 996

996 is an even number, because it is evenly divisible by 2: 996 / 2 = 498.

Find out more:

What is an even number?

Is 996 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 996 is about 31.559.

Thus, the square root of 996 is not an integer, and therefore 996 is not a square number.

What is the square number of 996?

The square of a number (here 996) is the result of the product of this number (996) by itself (i.e., 996 × 996); the square of 996 is sometimes called "raising 996 to the power 2", or "996 squared".

The square of 996 is 992 016 because 996 × 996 = 996² = 992 016.

As a consequence, 996 is the square root of 992 016.

Number of digits of 996

996 is a number with 3 digits.

What are the multiples of 996?

The multiples of 996 are all integers evenly divisible by 996, that is all numbers such that the remainder of the division by 996 is zero. There are infinitely many multiples of 996. The smallest multiples of 996 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 996 too, since 0 × 996 = 0
996: indeed, 996 is a multiple of itself, since 996 is evenly divisible by 996 (we have 996 / 996 = 1, so the remainder of this division is indeed zero)
1 992: indeed, 1 992 = 996 × 2
2 988: indeed, 2 988 = 996 × 3
3 984: indeed, 3 984 = 996 × 4
4 980: indeed, 4 980 = 996 × 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 996). 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 31.559). 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 996

Preceding numbers: …994, 995
Following numbers: 997, 998…

Nearest numbers from 996

Preceding prime number: 991
Following prime number: 997