It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 103, the answer is: yes, 103 is a prime number because it has only two distinct divisors: 1 and itself (103).
As a consequence, 103 is only a multiple of 1 and 103..
Since 103 is a prime number, 103 is also a deficient number, that is to say 103 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 103 without 103 itself (that is 1, by definition!).
Parity of 103
103 is an odd number, because it is not evenly divisible by 2.
Is 103 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 103 is about 10.149.
Thus, the square root of 103 is not an integer, and therefore 103 is not a square number.
Anyway, 103 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 103?
The square of a number (here 103) is the result of the product of this number (103) by itself (i.e., 103 × 103); the square of 103 is sometimes called "raising 103 to the power 2", or "103 squared".
As a consequence, 103 is the square root of 10 609.
Number of digits of 103
103 is a number with 3 digits.
What are the multiples of 103?
The multiples of 103 are all integers evenly divisible by 103, that is all numbers such that the remainder of the division by 103 is zero. There are infinitely many multiples of 103. The smallest multiples of 103 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 103 too, since 0 × 103 = 0
- 103: indeed, 103 is a multiple of itself, since 103 is evenly divisible by 103 (we have 103 / 103 = 1, so the remainder of this division is indeed zero)
- 206: indeed, 206 = 103 × 2
- 309: indeed, 309 = 103 × 3
- 412: indeed, 412 = 103 × 4
- 515: indeed, 515 = 103 × 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 103). 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 10.149). 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.