It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 491, the answer is: yes, 491 is a prime number because it has only two distinct divisors: 1 and itself (491).
As a consequence, 491 is only a multiple of 1 and 491..
Since 491 is a prime number, 491 is also a deficient number, that is to say 491 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 491 without 491 itself (that is 1, by definition!).
Parity of 491
491 is an odd number, because it is not evenly divisible by 2.
Is 491 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 491 is about 22.159.
Thus, the square root of 491 is not an integer, and therefore 491 is not a square number.
Anyway, 491 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 491?
The square of a number (here 491) is the result of the product of this number (491) by itself (i.e., 491 × 491); the square of 491 is sometimes called "raising 491 to the power 2", or "491 squared".
As a consequence, 491 is the square root of 241 081.
Number of digits of 491
491 is a number with 3 digits.
What are the multiples of 491?
The multiples of 491 are all integers evenly divisible by 491, that is all numbers such that the remainder of the division by 491 is zero. There are infinitely many multiples of 491. The smallest multiples of 491 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 491 too, since 0 × 491 = 0
- 491: indeed, 491 is a multiple of itself, since 491 is evenly divisible by 491 (we have 491 / 491 = 1, so the remainder of this division is indeed zero)
- 982: indeed, 982 = 491 × 2
- 1 473: indeed, 1 473 = 491 × 3
- 1 964: indeed, 1 964 = 491 × 4
- 2 455: indeed, 2 455 = 491 × 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 491). 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 22.159). 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.