It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 607, the answer is: yes, 607 is a prime number because it has only two distinct divisors: 1 and itself (607).
As a consequence, 607 is only a multiple of 1 and 607..
Since 607 is a prime number, 607 is also a deficient number, that is to say 607 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 607 without 607 itself (that is 1, by definition!).
Parity of 607
607 is an odd number, because it is not evenly divisible by 2.
Is 607 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 607 is about 24.637.
Thus, the square root of 607 is not an integer, and therefore 607 is not a square number.
Anyway, 607 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 607?
The square of a number (here 607) is the result of the product of this number (607) by itself (i.e., 607 × 607); the square of 607 is sometimes called "raising 607 to the power 2", or "607 squared".
As a consequence, 607 is the square root of 368 449.
Number of digits of 607
607 is a number with 3 digits.
What are the multiples of 607?
The multiples of 607 are all integers evenly divisible by 607, that is all numbers such that the remainder of the division by 607 is zero. There are infinitely many multiples of 607. The smallest multiples of 607 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 607 too, since 0 × 607 = 0
- 607: indeed, 607 is a multiple of itself, since 607 is evenly divisible by 607 (we have 607 / 607 = 1, so the remainder of this division is indeed zero)
- 1 214: indeed, 1 214 = 607 × 2
- 1 821: indeed, 1 821 = 607 × 3
- 2 428: indeed, 2 428 = 607 × 4
- 3 035: indeed, 3 035 = 607 × 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 607). 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 24.637). 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.