It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 673, the answer is: yes, 673 is a prime number because it has only two distinct divisors: 1 and itself (673).
As a consequence, 673 is only a multiple of 1 and 673..
Since 673 is a prime number, 673 is also a deficient number, that is to say 673 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 673 without 673 itself (that is 1, by definition!).
Parity of 673
673 is an odd number, because it is not evenly divisible by 2.
Is 673 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 673 is about 25.942.
Thus, the square root of 673 is not an integer, and therefore 673 is not a square number.
Anyway, 673 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 673?
The square of a number (here 673) is the result of the product of this number (673) by itself (i.e., 673 × 673); the square of 673 is sometimes called "raising 673 to the power 2", or "673 squared".
As a consequence, 673 is the square root of 452 929.
Number of digits of 673
673 is a number with 3 digits.
What are the multiples of 673?
The multiples of 673 are all integers evenly divisible by 673, that is all numbers such that the remainder of the division by 673 is zero. There are infinitely many multiples of 673. The smallest multiples of 673 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 673 too, since 0 × 673 = 0
- 673: indeed, 673 is a multiple of itself, since 673 is evenly divisible by 673 (we have 673 / 673 = 1, so the remainder of this division is indeed zero)
- 1 346: indeed, 1 346 = 673 × 2
- 2 019: indeed, 2 019 = 673 × 3
- 2 692: indeed, 2 692 = 673 × 4
- 3 365: indeed, 3 365 = 673 × 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 673). 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 25.942). 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.