It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 617, the answer is: yes, 617 is a prime number because it has only two distinct divisors: 1 and itself (617).
As a consequence, 617 is only a multiple of 1 and 617..
Since 617 is a prime number, 617 is also a deficient number, that is to say 617 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 617 without 617 itself (that is 1, by definition!).
Parity of 617
617 is an odd number, because it is not evenly divisible by 2.
Is 617 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 617 is about 24.839.
Thus, the square root of 617 is not an integer, and therefore 617 is not a square number.
Anyway, 617 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 617?
The square of a number (here 617) is the result of the product of this number (617) by itself (i.e., 617 × 617); the square of 617 is sometimes called "raising 617 to the power 2", or "617 squared".
As a consequence, 617 is the square root of 380 689.
Number of digits of 617
617 is a number with 3 digits.
What are the multiples of 617?
The multiples of 617 are all integers evenly divisible by 617, that is all numbers such that the remainder of the division by 617 is zero. There are infinitely many multiples of 617. The smallest multiples of 617 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 617 too, since 0 × 617 = 0
- 617: indeed, 617 is a multiple of itself, since 617 is evenly divisible by 617 (we have 617 / 617 = 1, so the remainder of this division is indeed zero)
- 1 234: indeed, 1 234 = 617 × 2
- 1 851: indeed, 1 851 = 617 × 3
- 2 468: indeed, 2 468 = 617 × 4
- 3 085: indeed, 3 085 = 617 × 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 617). 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 24.839). 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.