Is 816 a prime number?

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

For 816, the answer is: No, 816 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 816) is as follows: 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816.

For 816 to be a prime number, it would have been required that 816 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

816 is a multiple of 1
816 is a multiple of 2
816 is a multiple of 3
816 is a multiple of 4
816 is a multiple of 6
816 is a multiple of 8
816 is a multiple of 12
816 is a multiple of 16
816 is a multiple of 17
816 is a multiple of 24
816 is a multiple of 34
816 is a multiple of 48
816 is a multiple of 51
816 is a multiple of 68
816 is a multiple of 102
816 is a multiple of 136
816 is a multiple of 204
816 is a multiple of 272
816 is a multiple of 408

For 816 to be a prime number, it would have been required that 816 has only two divisors, i.e., itself and 1.

Is 816 a deficient number?

No, 816 is not a deficient number: to be deficient, 816 should have been such that 816 is larger than the sum of its proper divisors, i.e., the divisors of 816 without 816 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 17 + 24 + 34 + 48 + 51 + 68 + 102 + 136 + 204 + 272 + 408 = 1 416).

In fact, 816 is an abundant number; 816 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 17 + 24 + 34 + 48 + 51 + 68 + 102 + 136 + 204 + 272 + 408 = 1 416). The smallest abundant number is 12.

Parity of 816

816 is an even number, because it is evenly divisible by 2: 816 / 2 = 408.

Find out more:

What is an even number?

Is 816 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 816 is about 28.566.

Thus, the square root of 816 is not an integer, and therefore 816 is not a square number.

What is the square number of 816?

The square of a number (here 816) is the result of the product of this number (816) by itself (i.e., 816 × 816); the square of 816 is sometimes called "raising 816 to the power 2", or "816 squared".

The square of 816 is 665 856 because 816 × 816 = 816² = 665 856.

As a consequence, 816 is the square root of 665 856.

Number of digits of 816

816 is a number with 3 digits.

What are the multiples of 816?

The multiples of 816 are all integers evenly divisible by 816, that is all numbers such that the remainder of the division by 816 is zero. There are infinitely many multiples of 816. The smallest multiples of 816 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 816 too, since 0 × 816 = 0
816: indeed, 816 is a multiple of itself, since 816 is evenly divisible by 816 (we have 816 / 816 = 1, so the remainder of this division is indeed zero)
1 632: indeed, 1 632 = 816 × 2
2 448: indeed, 2 448 = 816 × 3
3 264: indeed, 3 264 = 816 × 4
4 080: indeed, 4 080 = 816 × 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 816). 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 28.566). 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 816

Preceding numbers: …814, 815
Following numbers: 817, 818…

Nearest numbers from 816

Preceding prime number: 811
Following prime number: 821