It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 743, the answer is: yes, 743 is a prime number because it has only two distinct divisors: 1 and itself (743).
As a consequence, 743 is only a multiple of 1 and 743..
Since 743 is a prime number, 743 is also a deficient number, that is to say 743 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 743 without 743 itself (that is 1, by definition!).
Parity of 743
743 is an odd number, because it is not evenly divisible by 2.
Is 743 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 743 is about 27.258.
Thus, the square root of 743 is not an integer, and therefore 743 is not a square number.
Anyway, 743 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 743?
The square of a number (here 743) is the result of the product of this number (743) by itself (i.e., 743 × 743); the square of 743 is sometimes called "raising 743 to the power 2", or "743 squared".
As a consequence, 743 is the square root of 552 049.
Number of digits of 743
743 is a number with 3 digits.
What are the multiples of 743?
The multiples of 743 are all integers evenly divisible by 743, that is all numbers such that the remainder of the division by 743 is zero. There are infinitely many multiples of 743. The smallest multiples of 743 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 743 too, since 0 × 743 = 0
- 743: indeed, 743 is a multiple of itself, since 743 is evenly divisible by 743 (we have 743 / 743 = 1, so the remainder of this division is indeed zero)
- 1 486: indeed, 1 486 = 743 × 2
- 2 229: indeed, 2 229 = 743 × 3
- 2 972: indeed, 2 972 = 743 × 4
- 3 715: indeed, 3 715 = 743 × 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 743). 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 27.258). 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.