It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 113, the answer is: yes, 113 is a prime number because it has only two distinct divisors: 1 and itself (113).
As a consequence, 113 is only a multiple of 1 and 113..
Since 113 is a prime number, 113 is also a deficient number, that is to say 113 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 113 without 113 itself (that is 1, by definition!).
Parity of 113
113 is an odd number, because it is not evenly divisible by 2.
Is 113 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 113 is about 10.630.
Thus, the square root of 113 is not an integer, and therefore 113 is not a square number.
Anyway, 113 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 113?
The square of a number (here 113) is the result of the product of this number (113) by itself (i.e., 113 × 113); the square of 113 is sometimes called "raising 113 to the power 2", or "113 squared".
As a consequence, 113 is the square root of 12 769.
Number of digits of 113
113 is a number with 3 digits.
What are the multiples of 113?
The multiples of 113 are all integers evenly divisible by 113, that is all numbers such that the remainder of the division by 113 is zero. There are infinitely many multiples of 113. The smallest multiples of 113 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 113 too, since 0 × 113 = 0
- 113: indeed, 113 is a multiple of itself, since 113 is evenly divisible by 113 (we have 113 / 113 = 1, so the remainder of this division is indeed zero)
- 226: indeed, 226 = 113 × 2
- 339: indeed, 339 = 113 × 3
- 452: indeed, 452 = 113 × 4
- 565: indeed, 565 = 113 × 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 113). 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 10.630). 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.