It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 761, the answer is: yes, 761 is a prime number because it has only two distinct divisors: 1 and itself (761).
As a consequence, 761 is only a multiple of 1 and 761..
Since 761 is a prime number, 761 is also a deficient number, that is to say 761 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 761 without 761 itself (that is 1, by definition!).
Parity of 761
761 is an odd number, because it is not evenly divisible by 2.
Is 761 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 761 is about 27.586.
Thus, the square root of 761 is not an integer, and therefore 761 is not a square number.
Anyway, 761 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 761?
The square of a number (here 761) is the result of the product of this number (761) by itself (i.e., 761 × 761); the square of 761 is sometimes called "raising 761 to the power 2", or "761 squared".
As a consequence, 761 is the square root of 579 121.
Number of digits of 761
761 is a number with 3 digits.
What are the multiples of 761?
The multiples of 761 are all integers evenly divisible by 761, that is all numbers such that the remainder of the division by 761 is zero. There are infinitely many multiples of 761. The smallest multiples of 761 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 761 too, since 0 × 761 = 0
- 761: indeed, 761 is a multiple of itself, since 761 is evenly divisible by 761 (we have 761 / 761 = 1, so the remainder of this division is indeed zero)
- 1 522: indeed, 1 522 = 761 × 2
- 2 283: indeed, 2 283 = 761 × 3
- 3 044: indeed, 3 044 = 761 × 4
- 3 805: indeed, 3 805 = 761 × 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 761). 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 27.586). 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.