It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 283, the answer is: yes, 283 is a prime number because it has only two distinct divisors: 1 and itself (283).
As a consequence, 283 is only a multiple of 1 and 283..
Since 283 is a prime number, 283 is also a deficient number, that is to say 283 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 283 without 283 itself (that is 1, by definition!).
Parity of 283
283 is an odd number, because it is not evenly divisible by 2.
Is 283 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 283 is about 16.823.
Thus, the square root of 283 is not an integer, and therefore 283 is not a square number.
Anyway, 283 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 283?
The square of a number (here 283) is the result of the product of this number (283) by itself (i.e., 283 × 283); the square of 283 is sometimes called "raising 283 to the power 2", or "283 squared".
As a consequence, 283 is the square root of 80 089.
Number of digits of 283
283 is a number with 3 digits.
What are the multiples of 283?
The multiples of 283 are all integers evenly divisible by 283, that is all numbers such that the remainder of the division by 283 is zero. There are infinitely many multiples of 283. The smallest multiples of 283 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 283 too, since 0 × 283 = 0
- 283: indeed, 283 is a multiple of itself, since 283 is evenly divisible by 283 (we have 283 / 283 = 1, so the remainder of this division is indeed zero)
- 566: indeed, 566 = 283 × 2
- 849: indeed, 849 = 283 × 3
- 1 132: indeed, 1 132 = 283 × 4
- 1 415: indeed, 1 415 = 283 × 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 283). 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 16.823). 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.