Is 891 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 891, the answer is: No, 891 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 891) is as follows: 1, 3, 9, 11, 27, 33, 81, 99, 297, 891.

For 891 to be a prime number, it would have been required that 891 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

891 is a multiple of 1
891 is a multiple of 3
891 is a multiple of 9
891 is a multiple of 11
891 is a multiple of 27
891 is a multiple of 33
891 is a multiple of 81
891 is a multiple of 99
891 is a multiple of 297

For 891 to be a prime number, it would have been required that 891 has only two divisors, i.e., itself and 1.

Is 891 a deficient number?

Yes, 891 is a deficient number, that is to say 891 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 891 without 891 itself (that is 1 + 3 + 9 + 11 + 27 + 33 + 81 + 99 + 297 = 561).

Parity of 891

891 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 891 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 891 is about 29.850.

Thus, the square root of 891 is not an integer, and therefore 891 is not a square number.

What is the square number of 891?

The square of a number (here 891) is the result of the product of this number (891) by itself (i.e., 891 × 891); the square of 891 is sometimes called "raising 891 to the power 2", or "891 squared".

The square of 891 is 793 881 because 891 × 891 = 891² = 793 881.

As a consequence, 891 is the square root of 793 881.

Number of digits of 891

891 is a number with 3 digits.

What are the multiples of 891?

The multiples of 891 are all integers evenly divisible by 891, that is all numbers such that the remainder of the division by 891 is zero. There are infinitely many multiples of 891. The smallest multiples of 891 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 891 too, since 0 × 891 = 0
891: indeed, 891 is a multiple of itself, since 891 is evenly divisible by 891 (we have 891 / 891 = 1, so the remainder of this division is indeed zero)
1 782: indeed, 1 782 = 891 × 2
2 673: indeed, 2 673 = 891 × 3
3 564: indeed, 3 564 = 891 × 4
4 455: indeed, 4 455 = 891 × 5
etc.

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 891). 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 29.850). 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.

Numbers near 891

Preceding numbers: …889, 890
Following numbers: 892, 893…

Nearest numbers from 891

Preceding prime number: 887
Following prime number: 907