Is 868 a prime number?

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

For 868, the answer is: No, 868 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 868) is as follows: 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.

For 868 to be a prime number, it would have been required that 868 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

868 is a multiple of 1
868 is a multiple of 2
868 is a multiple of 4
868 is a multiple of 7
868 is a multiple of 14
868 is a multiple of 28
868 is a multiple of 31
868 is a multiple of 62
868 is a multiple of 124
868 is a multiple of 217
868 is a multiple of 434

For 868 to be a prime number, it would have been required that 868 has only two divisors, i.e., itself and 1.

Is 868 a deficient number?

No, 868 is not a deficient number: to be deficient, 868 should have been such that 868 is larger than the sum of its proper divisors, i.e., the divisors of 868 without 868 itself (that is 1 + 2 + 4 + 7 + 14 + 28 + 31 + 62 + 124 + 217 + 434 = 924).

In fact, 868 is an abundant number; 868 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 14 + 28 + 31 + 62 + 124 + 217 + 434 = 924). The smallest abundant number is 12.

Parity of 868

868 is an even number, because it is evenly divisible by 2: 868 / 2 = 434.

Find out more:

What is an even number?

Is 868 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 868 is about 29.462.

Thus, the square root of 868 is not an integer, and therefore 868 is not a square number.

What is the square number of 868?

The square of a number (here 868) is the result of the product of this number (868) by itself (i.e., 868 × 868); the square of 868 is sometimes called "raising 868 to the power 2", or "868 squared".

The square of 868 is 753 424 because 868 × 868 = 868² = 753 424.

As a consequence, 868 is the square root of 753 424.

Number of digits of 868

868 is a number with 3 digits.

What are the multiples of 868?

The multiples of 868 are all integers evenly divisible by 868, that is all numbers such that the remainder of the division by 868 is zero. There are infinitely many multiples of 868. The smallest multiples of 868 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 868 too, since 0 × 868 = 0
868: indeed, 868 is a multiple of itself, since 868 is evenly divisible by 868 (we have 868 / 868 = 1, so the remainder of this division is indeed zero)
1 736: indeed, 1 736 = 868 × 2
2 604: indeed, 2 604 = 868 × 3
3 472: indeed, 3 472 = 868 × 4
4 340: indeed, 4 340 = 868 × 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 868). 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 29.462). 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 868

Preceding numbers: …866, 867
Following numbers: 869, 870…

Nearest numbers from 868

Preceding prime number: 863
Following prime number: 877