It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 773, the answer is: yes, 773 is a prime number because it has only two distinct divisors: 1 and itself (773).
As a consequence, 773 is only a multiple of 1 and 773..
Since 773 is a prime number, 773 is also a deficient number, that is to say 773 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 773 without 773 itself (that is 1, by definition!).
Parity of 773
773 is an odd number, because it is not evenly divisible by 2.
Is 773 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 773 is about 27.803.
Thus, the square root of 773 is not an integer, and therefore 773 is not a square number.
Anyway, 773 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 773?
The square of a number (here 773) is the result of the product of this number (773) by itself (i.e., 773 × 773); the square of 773 is sometimes called "raising 773 to the power 2", or "773 squared".
As a consequence, 773 is the square root of 597 529.
Number of digits of 773
773 is a number with 3 digits.
What are the multiples of 773?
The multiples of 773 are all integers evenly divisible by 773, that is all numbers such that the remainder of the division by 773 is zero. There are infinitely many multiples of 773. The smallest multiples of 773 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 773 too, since 0 × 773 = 0
- 773: indeed, 773 is a multiple of itself, since 773 is evenly divisible by 773 (we have 773 / 773 = 1, so the remainder of this division is indeed zero)
- 1 546: indeed, 1 546 = 773 × 2
- 2 319: indeed, 2 319 = 773 × 3
- 3 092: indeed, 3 092 = 773 × 4
- 3 865: indeed, 3 865 = 773 × 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 773). 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 27.803). 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.