It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 659, the answer is: yes, 659 is a prime number because it has only two distinct divisors: 1 and itself (659).
As a consequence, 659 is only a multiple of 1 and 659..
Since 659 is a prime number, 659 is also a deficient number, that is to say 659 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 659 without 659 itself (that is 1, by definition!).
Parity of 659
659 is an odd number, because it is not evenly divisible by 2.
Is 659 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 659 is about 25.671.
Thus, the square root of 659 is not an integer, and therefore 659 is not a square number.
Anyway, 659 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 659?
The square of a number (here 659) is the result of the product of this number (659) by itself (i.e., 659 × 659); the square of 659 is sometimes called "raising 659 to the power 2", or "659 squared".
As a consequence, 659 is the square root of 434 281.
Number of digits of 659
659 is a number with 3 digits.
What are the multiples of 659?
The multiples of 659 are all integers evenly divisible by 659, that is all numbers such that the remainder of the division by 659 is zero. There are infinitely many multiples of 659. The smallest multiples of 659 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 659 too, since 0 × 659 = 0
- 659: indeed, 659 is a multiple of itself, since 659 is evenly divisible by 659 (we have 659 / 659 = 1, so the remainder of this division is indeed zero)
- 1 318: indeed, 1 318 = 659 × 2
- 1 977: indeed, 1 977 = 659 × 3
- 2 636: indeed, 2 636 = 659 × 4
- 3 295: indeed, 3 295 = 659 × 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 659). 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 25.671). 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.