Is 826 a prime number?

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

For 826, the answer is: No, 826 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 826) is as follows: 1, 2, 7, 14, 59, 118, 413, 826.

For 826 to be a prime number, it would have been required that 826 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

826 is a multiple of 1
826 is a multiple of 2
826 is a multiple of 7
826 is a multiple of 14
826 is a multiple of 59
826 is a multiple of 118
826 is a multiple of 413

For 826 to be a prime number, it would have been required that 826 has only two divisors, i.e., itself and 1.

Is 826 a deficient number?

Yes, 826 is a deficient number, that is to say 826 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 826 without 826 itself (that is 1 + 2 + 7 + 14 + 59 + 118 + 413 = 614).

Parity of 826

826 is an even number, because it is evenly divisible by 2: 826 / 2 = 413.

Find out more:

What is an even number?

Is 826 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 826 is about 28.740.

Thus, the square root of 826 is not an integer, and therefore 826 is not a square number.

What is the square number of 826?

The square of a number (here 826) is the result of the product of this number (826) by itself (i.e., 826 × 826); the square of 826 is sometimes called "raising 826 to the power 2", or "826 squared".

The square of 826 is 682 276 because 826 × 826 = 826² = 682 276.

As a consequence, 826 is the square root of 682 276.

Number of digits of 826

826 is a number with 3 digits.

What are the multiples of 826?

The multiples of 826 are all integers evenly divisible by 826, that is all numbers such that the remainder of the division by 826 is zero. There are infinitely many multiples of 826. The smallest multiples of 826 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 826 too, since 0 × 826 = 0
826: indeed, 826 is a multiple of itself, since 826 is evenly divisible by 826 (we have 826 / 826 = 1, so the remainder of this division is indeed zero)
1 652: indeed, 1 652 = 826 × 2
2 478: indeed, 2 478 = 826 × 3
3 304: indeed, 3 304 = 826 × 4
4 130: indeed, 4 130 = 826 × 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 826). 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 28.740). 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 826

Preceding numbers: …824, 825
Following numbers: 827, 828…

Nearest numbers from 826

Preceding prime number: 823
Following prime number: 827