It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 587, the answer is: yes, 587 is a prime number because it has only two distinct divisors: 1 and itself (587).
As a consequence, 587 is only a multiple of 1 and 587..
Since 587 is a prime number, 587 is also a deficient number, that is to say 587 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 587 without 587 itself (that is 1, by definition!).
Parity of 587
587 is an odd number, because it is not evenly divisible by 2.
Is 587 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 587 is about 24.228.
Thus, the square root of 587 is not an integer, and therefore 587 is not a square number.
Anyway, 587 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 587?
The square of a number (here 587) is the result of the product of this number (587) by itself (i.e., 587 × 587); the square of 587 is sometimes called "raising 587 to the power 2", or "587 squared".
As a consequence, 587 is the square root of 344 569.
Number of digits of 587
587 is a number with 3 digits.
What are the multiples of 587?
The multiples of 587 are all integers evenly divisible by 587, that is all numbers such that the remainder of the division by 587 is zero. There are infinitely many multiples of 587. The smallest multiples of 587 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 587 too, since 0 × 587 = 0
- 587: indeed, 587 is a multiple of itself, since 587 is evenly divisible by 587 (we have 587 / 587 = 1, so the remainder of this division is indeed zero)
- 1 174: indeed, 1 174 = 587 × 2
- 1 761: indeed, 1 761 = 587 × 3
- 2 348: indeed, 2 348 = 587 × 4
- 2 935: indeed, 2 935 = 587 × 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 587). 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 24.228). 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.