It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 991, the answer is: yes, 991 is a prime number because it has only two distinct divisors: 1 and itself (991).
As a consequence, 991 is only a multiple of 1 and 991..
Since 991 is a prime number, 991 is also a deficient number, that is to say 991 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 991 without 991 itself (that is 1, by definition!).
Parity of 991
991 is an odd number, because it is not evenly divisible by 2.
Is 991 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 991 is about 31.480.
Thus, the square root of 991 is not an integer, and therefore 991 is not a square number.
Anyway, 991 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 991?
The square of a number (here 991) is the result of the product of this number (991) by itself (i.e., 991 × 991); the square of 991 is sometimes called "raising 991 to the power 2", or "991 squared".
As a consequence, 991 is the square root of 982 081.
Number of digits of 991
991 is a number with 3 digits.
What are the multiples of 991?
The multiples of 991 are all integers evenly divisible by 991, that is all numbers such that the remainder of the division by 991 is zero. There are infinitely many multiples of 991. The smallest multiples of 991 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 991 too, since 0 × 991 = 0
- 991: indeed, 991 is a multiple of itself, since 991 is evenly divisible by 991 (we have 991 / 991 = 1, so the remainder of this division is indeed zero)
- 1 982: indeed, 1 982 = 991 × 2
- 2 973: indeed, 2 973 = 991 × 3
- 3 964: indeed, 3 964 = 991 × 4
- 4 955: indeed, 4 955 = 991 × 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 991). 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 31.480). 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.