Is 858 a prime number?

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

For 858, the answer is: No, 858 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 858) is as follows: 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858.

For 858 to be a prime number, it would have been required that 858 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

858 is a multiple of 1
858 is a multiple of 2
858 is a multiple of 3
858 is a multiple of 6
858 is a multiple of 11
858 is a multiple of 13
858 is a multiple of 22
858 is a multiple of 26
858 is a multiple of 33
858 is a multiple of 39
858 is a multiple of 66
858 is a multiple of 78
858 is a multiple of 143
858 is a multiple of 286
858 is a multiple of 429

For 858 to be a prime number, it would have been required that 858 has only two divisors, i.e., itself and 1.

Is 858 a deficient number?

No, 858 is not a deficient number: to be deficient, 858 should have been such that 858 is larger than the sum of its proper divisors, i.e., the divisors of 858 without 858 itself (that is 1 + 2 + 3 + 6 + 11 + 13 + 22 + 26 + 33 + 39 + 66 + 78 + 143 + 286 + 429 = 1 158).

In fact, 858 is an abundant number; 858 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 11 + 13 + 22 + 26 + 33 + 39 + 66 + 78 + 143 + 286 + 429 = 1 158). The smallest abundant number is 12.

Parity of 858

858 is an even number, because it is evenly divisible by 2: 858 / 2 = 429.

Find out more:

What is an even number?

Is 858 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 858 is about 29.292.

Thus, the square root of 858 is not an integer, and therefore 858 is not a square number.

What is the square number of 858?

The square of a number (here 858) is the result of the product of this number (858) by itself (i.e., 858 × 858); the square of 858 is sometimes called "raising 858 to the power 2", or "858 squared".

The square of 858 is 736 164 because 858 × 858 = 858² = 736 164.

As a consequence, 858 is the square root of 736 164.

Number of digits of 858

858 is a number with 3 digits.

What are the multiples of 858?

The multiples of 858 are all integers evenly divisible by 858, that is all numbers such that the remainder of the division by 858 is zero. There are infinitely many multiples of 858. The smallest multiples of 858 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 858 too, since 0 × 858 = 0
858: indeed, 858 is a multiple of itself, since 858 is evenly divisible by 858 (we have 858 / 858 = 1, so the remainder of this division is indeed zero)
1 716: indeed, 1 716 = 858 × 2
2 574: indeed, 2 574 = 858 × 3
3 432: indeed, 3 432 = 858 × 4
4 290: indeed, 4 290 = 858 × 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 858). 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 29.292). 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 858

Preceding numbers: …856, 857
Following numbers: 859, 860…

Nearest numbers from 858

Preceding prime number: 857
Following prime number: 859