Is 864 a prime number? What are the divisors of 864?

## Is 864 a prime number?

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

For 864, the answer is: No, 864 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 864) is as follows: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.

To be 864 a prime number, it would have been required that 864 has only two divisors, i.e., itself and 1.

As a consequence:

• 864 is a multiple of 1
• 864 is a multiple of 2
• 864 is a multiple of 3
• 864 is a multiple of 4
• 864 is a multiple of 6
• 864 is a multiple of 8
• 864 is a multiple of 9
• 864 is a multiple of 12
• 864 is a multiple of 16
• 864 is a multiple of 18
• 864 is a multiple of 24
• 864 is a multiple of 27
• 864 is a multiple of 32
• 864 is a multiple of 36
• 864 is a multiple of 48
• 864 is a multiple of 54
• 864 is a multiple of 72
• 864 is a multiple of 96
• 864 is a multiple of 108
• 864 is a multiple of 144
• 864 is a multiple of 216
• 864 is a multiple of 288
• 864 is a multiple of 432

To be 864 a prime number, it would have been required that 864 has only two divisors, i.e., itself and 1.

## Is 864 a deficient number?

No, 864 is not a deficient number: to be deficient, 864 should have been such that 864 is larger than the sum of its proper divisors, i.e., the divisors of 864 without 864 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 96 + 108 + 144 + 216 + 288 + 432 = 1 656).

In fact, 864 is an abundant number; 864 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 96 + 108 + 144 + 216 + 288 + 432 = 1 656). The smallest abundant number is 12.

## Parity of 864

864 is an even number, because it is evenly divisible by 2: 864 / 2 = 432.

## Is 864 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 864 is about 29.394.

Thus, the square root of 864 is not an integer, and therefore 864 is not a square number.

## What is the square number of 864?

The square of a number (here 864) is the result of the product of this number (864) by itself (i.e., 864 × 864); the square of 864 is sometimes called "raising 864 to the power 2", or "864 squared".

The square of 864 is 746 496 because 864 × 864 = 8642 = 746 496.

As a consequence, 864 is the square root of 746 496.

## Number of digits of 864

864 is a number with 3 digits.

## What are the multiples of 864?

The multiples of 864 are all integers evenly divisible by 864, that is all numbers such that the remainder of the division by 864 is zero. There are infinitely many multiples of 864. The smallest multiples of 864 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 864 too, since 0 × 864 = 0
• 864: indeed, 864 is a multiple of itself, since 864 is evenly divisible by 864 (we have 864 / 864 = 1, so the remainder of this division is indeed zero)
• 1 728: indeed, 1 728 = 864 × 2
• 2 592: indeed, 2 592 = 864 × 3
• 3 456: indeed, 3 456 = 864 × 4
• 4 320: indeed, 4 320 = 864 × 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 864). 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 29.394). 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 864

• Preceding numbers: …862, 863
• Following numbers: 865, 866

## Nearest numbers from 864

• Preceding prime number: 863
• Following prime number: 877
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