Is 846 a prime number?

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

For 846, the answer is: No, 846 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 846) is as follows: 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846.

For 846 to be a prime number, it would have been required that 846 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

846 is a multiple of 1
846 is a multiple of 2
846 is a multiple of 3
846 is a multiple of 6
846 is a multiple of 9
846 is a multiple of 18
846 is a multiple of 47
846 is a multiple of 94
846 is a multiple of 141
846 is a multiple of 282
846 is a multiple of 423

For 846 to be a prime number, it would have been required that 846 has only two divisors, i.e., itself and 1.

Is 846 a deficient number?

No, 846 is not a deficient number: to be deficient, 846 should have been such that 846 is larger than the sum of its proper divisors, i.e., the divisors of 846 without 846 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 47 + 94 + 141 + 282 + 423 = 1 026).

In fact, 846 is an abundant number; 846 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 47 + 94 + 141 + 282 + 423 = 1 026). The smallest abundant number is 12.

Parity of 846

846 is an even number, because it is evenly divisible by 2: 846 / 2 = 423.

Find out more:

What is an even number?

Is 846 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 846 is about 29.086.

Thus, the square root of 846 is not an integer, and therefore 846 is not a square number.

What is the square number of 846?

The square of a number (here 846) is the result of the product of this number (846) by itself (i.e., 846 × 846); the square of 846 is sometimes called "raising 846 to the power 2", or "846 squared".

The square of 846 is 715 716 because 846 × 846 = 846² = 715 716.

As a consequence, 846 is the square root of 715 716.

Number of digits of 846

846 is a number with 3 digits.

What are the multiples of 846?

The multiples of 846 are all integers evenly divisible by 846, that is all numbers such that the remainder of the division by 846 is zero. There are infinitely many multiples of 846. The smallest multiples of 846 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 846 too, since 0 × 846 = 0
846: indeed, 846 is a multiple of itself, since 846 is evenly divisible by 846 (we have 846 / 846 = 1, so the remainder of this division is indeed zero)
1 692: indeed, 1 692 = 846 × 2
2 538: indeed, 2 538 = 846 × 3
3 384: indeed, 3 384 = 846 × 4
4 230: indeed, 4 230 = 846 × 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 846). 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 29.086). 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 846

Preceding numbers: …844, 845
Following numbers: 847, 848…

Nearest numbers from 846

Preceding prime number: 839
Following prime number: 853