Is 871 a prime number?

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

For 871, the answer is: No, 871 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 871) is as follows: 1, 13, 67, 871.

For 871 to be a prime number, it would have been required that 871 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

871 is a multiple of 1
871 is a multiple of 13
871 is a multiple of 67

For 871 to be a prime number, it would have been required that 871 has only two divisors, i.e., itself and 1.

However, 871 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 871 = 13 x 67, where 13 and 67 are both prime numbers.

Is 871 a deficient number?

Yes, 871 is a deficient number, that is to say 871 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 871 without 871 itself (that is 1 + 13 + 67 = 81).

Parity of 871

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

Find out more:

What is an even number?

Is 871 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 871 is about 29.513.

Thus, the square root of 871 is not an integer, and therefore 871 is not a square number.

What is the square number of 871?

The square of a number (here 871) is the result of the product of this number (871) by itself (i.e., 871 × 871); the square of 871 is sometimes called "raising 871 to the power 2", or "871 squared".

The square of 871 is 758 641 because 871 × 871 = 871² = 758 641.

As a consequence, 871 is the square root of 758 641.

Number of digits of 871

871 is a number with 3 digits.

What are the multiples of 871?

The multiples of 871 are all integers evenly divisible by 871, that is all numbers such that the remainder of the division by 871 is zero. There are infinitely many multiples of 871. The smallest multiples of 871 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 871 too, since 0 × 871 = 0
871: indeed, 871 is a multiple of itself, since 871 is evenly divisible by 871 (we have 871 / 871 = 1, so the remainder of this division is indeed zero)
1 742: indeed, 1 742 = 871 × 2
2 613: indeed, 2 613 = 871 × 3
3 484: indeed, 3 484 = 871 × 4
4 355: indeed, 4 355 = 871 × 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 871). 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 29.513). 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 871

Preceding numbers: …869, 870
Following numbers: 872, 873…

Nearest numbers from 871

Preceding prime number: 863
Following prime number: 877