Is 814 a prime number?

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

For 814, the answer is: No, 814 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 814) is as follows: 1, 2, 11, 22, 37, 74, 407, 814.

For 814 to be a prime number, it would have been required that 814 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

814 is a multiple of 1
814 is a multiple of 2
814 is a multiple of 11
814 is a multiple of 22
814 is a multiple of 37
814 is a multiple of 74
814 is a multiple of 407

For 814 to be a prime number, it would have been required that 814 has only two divisors, i.e., itself and 1.

Is 814 a deficient number?

Yes, 814 is a deficient number, that is to say 814 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 814 without 814 itself (that is 1 + 2 + 11 + 22 + 37 + 74 + 407 = 554).

Parity of 814

814 is an even number, because it is evenly divisible by 2: 814 / 2 = 407.

Find out more:

What is an even number?

Is 814 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 814 is about 28.531.

Thus, the square root of 814 is not an integer, and therefore 814 is not a square number.

What is the square number of 814?

The square of a number (here 814) is the result of the product of this number (814) by itself (i.e., 814 × 814); the square of 814 is sometimes called "raising 814 to the power 2", or "814 squared".

The square of 814 is 662 596 because 814 × 814 = 814² = 662 596.

As a consequence, 814 is the square root of 662 596.

Number of digits of 814

814 is a number with 3 digits.

What are the multiples of 814?

The multiples of 814 are all integers evenly divisible by 814, that is all numbers such that the remainder of the division by 814 is zero. There are infinitely many multiples of 814. The smallest multiples of 814 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 814 too, since 0 × 814 = 0
814: indeed, 814 is a multiple of itself, since 814 is evenly divisible by 814 (we have 814 / 814 = 1, so the remainder of this division is indeed zero)
1 628: indeed, 1 628 = 814 × 2
2 442: indeed, 2 442 = 814 × 3
3 256: indeed, 3 256 = 814 × 4
4 070: indeed, 4 070 = 814 × 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 814). 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 28.531). 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 814

Preceding numbers: …812, 813
Following numbers: 815, 816…

Nearest numbers from 814

Preceding prime number: 811
Following prime number: 821