It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 173, the answer is: yes, 173 is a prime number because it has only two distinct divisors: 1 and itself (173).
As a consequence, 173 is only a multiple of 1 and 173..
Since 173 is a prime number, 173 is also a deficient number, that is to say 173 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 173 without 173 itself (that is 1, by definition!).
Parity of 173
173 is an odd number, because it is not evenly divisible by 2.
Is 173 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 173 is about 13.153.
Thus, the square root of 173 is not an integer, and therefore 173 is not a square number.
Anyway, 173 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 173?
The square of a number (here 173) is the result of the product of this number (173) by itself (i.e., 173 × 173); the square of 173 is sometimes called "raising 173 to the power 2", or "173 squared".
As a consequence, 173 is the square root of 29 929.
Number of digits of 173
173 is a number with 3 digits.
What are the multiples of 173?
The multiples of 173 are all integers evenly divisible by 173, that is all numbers such that the remainder of the division by 173 is zero. There are infinitely many multiples of 173. The smallest multiples of 173 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 173 too, since 0 × 173 = 0
- 173: indeed, 173 is a multiple of itself, since 173 is evenly divisible by 173 (we have 173 / 173 = 1, so the remainder of this division is indeed zero)
- 346: indeed, 346 = 173 × 2
- 519: indeed, 519 = 173 × 3
- 692: indeed, 692 = 173 × 4
- 865: indeed, 865 = 173 × 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 173). 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 13.153). 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.