Is 828 a prime number?

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

For 828, the answer is: No, 828 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 828) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.

For 828 to be a prime number, it would have been required that 828 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

828 is a multiple of 1
828 is a multiple of 2
828 is a multiple of 3
828 is a multiple of 4
828 is a multiple of 6
828 is a multiple of 9
828 is a multiple of 12
828 is a multiple of 18
828 is a multiple of 23
828 is a multiple of 36
828 is a multiple of 46
828 is a multiple of 69
828 is a multiple of 92
828 is a multiple of 138
828 is a multiple of 207
828 is a multiple of 276
828 is a multiple of 414

For 828 to be a prime number, it would have been required that 828 has only two divisors, i.e., itself and 1.

Is 828 a deficient number?

No, 828 is not a deficient number: to be deficient, 828 should have been such that 828 is larger than the sum of its proper divisors, i.e., the divisors of 828 without 828 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 23 + 36 + 46 + 69 + 92 + 138 + 207 + 276 + 414 = 1 356).

In fact, 828 is an abundant number; 828 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 23 + 36 + 46 + 69 + 92 + 138 + 207 + 276 + 414 = 1 356). The smallest abundant number is 12.

Parity of 828

828 is an even number, because it is evenly divisible by 2: 828 / 2 = 414.

Find out more:

What is an even number?

Is 828 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 828 is about 28.775.

Thus, the square root of 828 is not an integer, and therefore 828 is not a square number.

What is the square number of 828?

The square of a number (here 828) is the result of the product of this number (828) by itself (i.e., 828 × 828); the square of 828 is sometimes called "raising 828 to the power 2", or "828 squared".

The square of 828 is 685 584 because 828 × 828 = 828² = 685 584.

As a consequence, 828 is the square root of 685 584.

Number of digits of 828

828 is a number with 3 digits.

What are the multiples of 828?

The multiples of 828 are all integers evenly divisible by 828, that is all numbers such that the remainder of the division by 828 is zero. There are infinitely many multiples of 828. The smallest multiples of 828 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 828 too, since 0 × 828 = 0
828: indeed, 828 is a multiple of itself, since 828 is evenly divisible by 828 (we have 828 / 828 = 1, so the remainder of this division is indeed zero)
1 656: indeed, 1 656 = 828 × 2
2 484: indeed, 2 484 = 828 × 3
3 312: indeed, 3 312 = 828 × 4
4 140: indeed, 4 140 = 828 × 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 828). 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 28.775). 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 828

Preceding numbers: …826, 827
Following numbers: 829, 830…

Nearest numbers from 828

Preceding prime number: 827
Following prime number: 829