Is 861 a prime number?

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

For 861, the answer is: No, 861 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 861) is as follows: 1, 3, 7, 21, 41, 123, 287, 861.

For 861 to be a prime number, it would have been required that 861 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

861 is a multiple of 1
861 is a multiple of 3
861 is a multiple of 7
861 is a multiple of 21
861 is a multiple of 41
861 is a multiple of 123
861 is a multiple of 287

For 861 to be a prime number, it would have been required that 861 has only two divisors, i.e., itself and 1.

Is 861 a deficient number?

Yes, 861 is a deficient number, that is to say 861 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 861 without 861 itself (that is 1 + 3 + 7 + 21 + 41 + 123 + 287 = 483).

Parity of 861

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

Find out more:

What is an even number?

Is 861 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 861 is about 29.343.

Thus, the square root of 861 is not an integer, and therefore 861 is not a square number.

What is the square number of 861?

The square of a number (here 861) is the result of the product of this number (861) by itself (i.e., 861 × 861); the square of 861 is sometimes called "raising 861 to the power 2", or "861 squared".

The square of 861 is 741 321 because 861 × 861 = 861² = 741 321.

As a consequence, 861 is the square root of 741 321.

Number of digits of 861

861 is a number with 3 digits.

What are the multiples of 861?

The multiples of 861 are all integers evenly divisible by 861, that is all numbers such that the remainder of the division by 861 is zero. There are infinitely many multiples of 861. The smallest multiples of 861 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 861 too, since 0 × 861 = 0
861: indeed, 861 is a multiple of itself, since 861 is evenly divisible by 861 (we have 861 / 861 = 1, so the remainder of this division is indeed zero)
1 722: indeed, 1 722 = 861 × 2
2 583: indeed, 2 583 = 861 × 3
3 444: indeed, 3 444 = 861 × 4
4 305: indeed, 4 305 = 861 × 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 861). 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 29.343). 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 861

Preceding numbers: …859, 860
Following numbers: 862, 863…

Nearest numbers from 861

Preceding prime number: 859
Following prime number: 863