It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 733, the answer is: yes, 733 is a prime number because it has only two distinct divisors: 1 and itself (733).
As a consequence, 733 is only a multiple of 1 and 733..
Since 733 is a prime number, 733 is also a deficient number, that is to say 733 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 733 without 733 itself (that is 1, by definition!).
Parity of 733
733 is an odd number, because it is not evenly divisible by 2.
Is 733 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 733 is about 27.074.
Thus, the square root of 733 is not an integer, and therefore 733 is not a square number.
Anyway, 733 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 733?
The square of a number (here 733) is the result of the product of this number (733) by itself (i.e., 733 × 733); the square of 733 is sometimes called "raising 733 to the power 2", or "733 squared".
As a consequence, 733 is the square root of 537 289.
Number of digits of 733
733 is a number with 3 digits.
What are the multiples of 733?
The multiples of 733 are all integers evenly divisible by 733, that is all numbers such that the remainder of the division by 733 is zero. There are infinitely many multiples of 733. The smallest multiples of 733 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 733 too, since 0 × 733 = 0
- 733: indeed, 733 is a multiple of itself, since 733 is evenly divisible by 733 (we have 733 / 733 = 1, so the remainder of this division is indeed zero)
- 1 466: indeed, 1 466 = 733 × 2
- 2 199: indeed, 2 199 = 733 × 3
- 2 932: indeed, 2 932 = 733 × 4
- 3 665: indeed, 3 665 = 733 × 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 733). 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 27.074). 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.