It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 881, the answer is: yes, 881 is a prime number because it has only two distinct divisors: 1 and itself (881).
As a consequence, 881 is only a multiple of 1 and 881..
Since 881 is a prime number, 881 is also a deficient number, that is to say 881 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 881 without 881 itself (that is 1, by definition!).
Parity of 881
881 is an odd number, because it is not evenly divisible by 2.
Is 881 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 881 is about 29.682.
Thus, the square root of 881 is not an integer, and therefore 881 is not a square number.
Anyway, 881 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 881?
The square of a number (here 881) is the result of the product of this number (881) by itself (i.e., 881 × 881); the square of 881 is sometimes called "raising 881 to the power 2", or "881 squared".
As a consequence, 881 is the square root of 776 161.
Number of digits of 881
881 is a number with 3 digits.
What are the multiples of 881?
The multiples of 881 are all integers evenly divisible by 881, that is all numbers such that the remainder of the division by 881 is zero. There are infinitely many multiples of 881. The smallest multiples of 881 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 881 too, since 0 × 881 = 0
- 881: indeed, 881 is a multiple of itself, since 881 is evenly divisible by 881 (we have 881 / 881 = 1, so the remainder of this division is indeed zero)
- 1 762: indeed, 1 762 = 881 × 2
- 2 643: indeed, 2 643 = 881 × 3
- 3 524: indeed, 3 524 = 881 × 4
- 4 405: indeed, 4 405 = 881 × 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 881). 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 29.682). 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.