It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 859, the answer is: yes, 859 is a prime number because it has only two distinct divisors: 1 and itself (859).
As a consequence, 859 is only a multiple of 1 and 859..
Since 859 is a prime number, 859 is also a deficient number, that is to say 859 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 859 without 859 itself (that is 1, by definition!).
Parity of 859
859 is an odd number, because it is not evenly divisible by 2.
Is 859 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 859 is about 29.309.
Thus, the square root of 859 is not an integer, and therefore 859 is not a square number.
Anyway, 859 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 859?
The square of a number (here 859) is the result of the product of this number (859) by itself (i.e., 859 × 859); the square of 859 is sometimes called "raising 859 to the power 2", or "859 squared".
As a consequence, 859 is the square root of 737 881.
Number of digits of 859
859 is a number with 3 digits.
What are the multiples of 859?
The multiples of 859 are all integers evenly divisible by 859, that is all numbers such that the remainder of the division by 859 is zero. There are infinitely many multiples of 859. The smallest multiples of 859 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 859 too, since 0 × 859 = 0
- 859: indeed, 859 is a multiple of itself, since 859 is evenly divisible by 859 (we have 859 / 859 = 1, so the remainder of this division is indeed zero)
- 1 718: indeed, 1 718 = 859 × 2
- 2 577: indeed, 2 577 = 859 × 3
- 3 436: indeed, 3 436 = 859 × 4
- 4 295: indeed, 4 295 = 859 × 5
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 859). 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 29.309). 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.