It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 109, the answer is: yes, 109 is a prime number because it has only two distinct divisors: 1 and itself (109).
As a consequence, 109 is only a multiple of 1 and 109..
Since 109 is a prime number, 109 is also a deficient number, that is to say 109 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 109 without 109 itself (that is 1, by definition!).
Parity of 109
109 is an odd number, because it is not evenly divisible by 2.
Is 109 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 109 is about 10.440.
Thus, the square root of 109 is not an integer, and therefore 109 is not a square number.
Anyway, 109 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 109?
The square of a number (here 109) is the result of the product of this number (109) by itself (i.e., 109 × 109); the square of 109 is sometimes called "raising 109 to the power 2", or "109 squared".
As a consequence, 109 is the square root of 11 881.
Number of digits of 109
109 is a number with 3 digits.
What are the multiples of 109?
The multiples of 109 are all integers evenly divisible by 109, that is all numbers such that the remainder of the division by 109 is zero. There are infinitely many multiples of 109. The smallest multiples of 109 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 109 too, since 0 × 109 = 0
- 109: indeed, 109 is a multiple of itself, since 109 is evenly divisible by 109 (we have 109 / 109 = 1, so the remainder of this division is indeed zero)
- 218: indeed, 218 = 109 × 2
- 327: indeed, 327 = 109 × 3
- 436: indeed, 436 = 109 × 4
- 545: indeed, 545 = 109 × 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 109). 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 10.440). 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.