It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 613, the answer is: yes, 613 is a prime number because it has only two distinct divisors: 1 and itself (613).
As a consequence, 613 is only a multiple of 1 and 613..
Since 613 is a prime number, 613 is also a deficient number, that is to say 613 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 613 without 613 itself (that is 1, by definition!).
Parity of 613
613 is an odd number, because it is not evenly divisible by 2.
Is 613 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 613 is about 24.759.
Thus, the square root of 613 is not an integer, and therefore 613 is not a square number.
Anyway, 613 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 613?
The square of a number (here 613) is the result of the product of this number (613) by itself (i.e., 613 × 613); the square of 613 is sometimes called "raising 613 to the power 2", or "613 squared".
As a consequence, 613 is the square root of 375 769.
Number of digits of 613
613 is a number with 3 digits.
What are the multiples of 613?
The multiples of 613 are all integers evenly divisible by 613, that is all numbers such that the remainder of the division by 613 is zero. There are infinitely many multiples of 613. The smallest multiples of 613 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 613 too, since 0 × 613 = 0
- 613: indeed, 613 is a multiple of itself, since 613 is evenly divisible by 613 (we have 613 / 613 = 1, so the remainder of this division is indeed zero)
- 1 226: indeed, 1 226 = 613 × 2
- 1 839: indeed, 1 839 = 613 × 3
- 2 452: indeed, 2 452 = 613 × 4
- 3 065: indeed, 3 065 = 613 × 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 613). 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 24.759). 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.