It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 373, the answer is: yes, 373 is a prime number because it has only two distinct divisors: 1 and itself (373).
As a consequence, 373 is only a multiple of 1 and 373..
Since 373 is a prime number, 373 is also a deficient number, that is to say 373 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 373 without 373 itself (that is 1, by definition!).
Parity of 373
373 is an odd number, because it is not evenly divisible by 2.
Is 373 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 373 is about 19.313.
Thus, the square root of 373 is not an integer, and therefore 373 is not a square number.
Anyway, 373 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 373?
The square of a number (here 373) is the result of the product of this number (373) by itself (i.e., 373 × 373); the square of 373 is sometimes called "raising 373 to the power 2", or "373 squared".
As a consequence, 373 is the square root of 139 129.
Number of digits of 373
373 is a number with 3 digits.
What are the multiples of 373?
The multiples of 373 are all integers evenly divisible by 373, that is all numbers such that the remainder of the division by 373 is zero. There are infinitely many multiples of 373. The smallest multiples of 373 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 373 too, since 0 × 373 = 0
- 373: indeed, 373 is a multiple of itself, since 373 is evenly divisible by 373 (we have 373 / 373 = 1, so the remainder of this division is indeed zero)
- 746: indeed, 746 = 373 × 2
- 1 119: indeed, 1 119 = 373 × 3
- 1 492: indeed, 1 492 = 373 × 4
- 1 865: indeed, 1 865 = 373 × 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 373). 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 19.313). 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.