Is 813 a prime number?

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

For 813, the answer is: No, 813 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 813) is as follows: 1, 3, 271, 813.

For 813 to be a prime number, it would have been required that 813 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

813 is a multiple of 1
813 is a multiple of 3
813 is a multiple of 271

For 813 to be a prime number, it would have been required that 813 has only two divisors, i.e., itself and 1.

However, 813 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 813 = 3 x 271, where 3 and 271 are both prime numbers.

Is 813 a deficient number?

Yes, 813 is a deficient number, that is to say 813 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 813 without 813 itself (that is 1 + 3 + 271 = 275).

Parity of 813

813 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 813 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 813 is about 28.513.

Thus, the square root of 813 is not an integer, and therefore 813 is not a square number.

What is the square number of 813?

The square of a number (here 813) is the result of the product of this number (813) by itself (i.e., 813 × 813); the square of 813 is sometimes called "raising 813 to the power 2", or "813 squared".

The square of 813 is 660 969 because 813 × 813 = 813² = 660 969.

As a consequence, 813 is the square root of 660 969.

Number of digits of 813

813 is a number with 3 digits.

What are the multiples of 813?

The multiples of 813 are all integers evenly divisible by 813, that is all numbers such that the remainder of the division by 813 is zero. There are infinitely many multiples of 813. The smallest multiples of 813 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 813 too, since 0 × 813 = 0
813: indeed, 813 is a multiple of itself, since 813 is evenly divisible by 813 (we have 813 / 813 = 1, so the remainder of this division is indeed zero)
1 626: indeed, 1 626 = 813 × 2
2 439: indeed, 2 439 = 813 × 3
3 252: indeed, 3 252 = 813 × 4
4 065: indeed, 4 065 = 813 × 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 813). 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 28.513). 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 813

Preceding numbers: …811, 812
Following numbers: 814, 815…

Nearest numbers from 813

Preceding prime number: 811
Following prime number: 821