It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 787, the answer is: yes, 787 is a prime number because it has only two distinct divisors: 1 and itself (787).
As a consequence, 787 is only a multiple of 1 and 787..
Since 787 is a prime number, 787 is also a deficient number, that is to say 787 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 787 without 787 itself (that is 1, by definition!).
Parity of 787
787 is an odd number, because it is not evenly divisible by 2.
Is 787 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 787 is about 28.054.
Thus, the square root of 787 is not an integer, and therefore 787 is not a square number.
Anyway, 787 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 787?
The square of a number (here 787) is the result of the product of this number (787) by itself (i.e., 787 × 787); the square of 787 is sometimes called "raising 787 to the power 2", or "787 squared".
As a consequence, 787 is the square root of 619 369.
Number of digits of 787
787 is a number with 3 digits.
What are the multiples of 787?
The multiples of 787 are all integers evenly divisible by 787, that is all numbers such that the remainder of the division by 787 is zero. There are infinitely many multiples of 787. The smallest multiples of 787 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 787 too, since 0 × 787 = 0
- 787: indeed, 787 is a multiple of itself, since 787 is evenly divisible by 787 (we have 787 / 787 = 1, so the remainder of this division is indeed zero)
- 1 574: indeed, 1 574 = 787 × 2
- 2 361: indeed, 2 361 = 787 × 3
- 3 148: indeed, 3 148 = 787 × 4
- 3 935: indeed, 3 935 = 787 × 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 787). 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 28.054). 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.