Is 872 a prime number?

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

For 872, the answer is: No, 872 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 872) is as follows: 1, 2, 4, 8, 109, 218, 436, 872.

For 872 to be a prime number, it would have been required that 872 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

872 is a multiple of 1
872 is a multiple of 2
872 is a multiple of 4
872 is a multiple of 8
872 is a multiple of 109
872 is a multiple of 218
872 is a multiple of 436

For 872 to be a prime number, it would have been required that 872 has only two divisors, i.e., itself and 1.

Is 872 a deficient number?

Yes, 872 is a deficient number, that is to say 872 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 872 without 872 itself (that is 1 + 2 + 4 + 8 + 109 + 218 + 436 = 778).

Parity of 872

872 is an even number, because it is evenly divisible by 2: 872 / 2 = 436.

Find out more:

What is an even number?

Is 872 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 872 is about 29.530.

Thus, the square root of 872 is not an integer, and therefore 872 is not a square number.

What is the square number of 872?

The square of a number (here 872) is the result of the product of this number (872) by itself (i.e., 872 × 872); the square of 872 is sometimes called "raising 872 to the power 2", or "872 squared".

The square of 872 is 760 384 because 872 × 872 = 872² = 760 384.

As a consequence, 872 is the square root of 760 384.

Number of digits of 872

872 is a number with 3 digits.

What are the multiples of 872?

The multiples of 872 are all integers evenly divisible by 872, that is all numbers such that the remainder of the division by 872 is zero. There are infinitely many multiples of 872. The smallest multiples of 872 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 872 too, since 0 × 872 = 0
872: indeed, 872 is a multiple of itself, since 872 is evenly divisible by 872 (we have 872 / 872 = 1, so the remainder of this division is indeed zero)
1 744: indeed, 1 744 = 872 × 2
2 616: indeed, 2 616 = 872 × 3
3 488: indeed, 3 488 = 872 × 4
4 360: indeed, 4 360 = 872 × 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 872). 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 29.530). 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 872

Preceding numbers: …870, 871
Following numbers: 873, 874…

Nearest numbers from 872

Preceding prime number: 863
Following prime number: 877