It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 829, the answer is: yes, 829 is a prime number because it has only two distinct divisors: 1 and itself (829).
As a consequence, 829 is only a multiple of 1 and 829..
Since 829 is a prime number, 829 is also a deficient number, that is to say 829 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 829 without 829 itself (that is 1, by definition!).
Parity of 829
829 is an odd number, because it is not evenly divisible by 2.
Is 829 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 829 is about 28.792.
Thus, the square root of 829 is not an integer, and therefore 829 is not a square number.
Anyway, 829 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 829?
The square of a number (here 829) is the result of the product of this number (829) by itself (i.e., 829 × 829); the square of 829 is sometimes called "raising 829 to the power 2", or "829 squared".
As a consequence, 829 is the square root of 687 241.
Number of digits of 829
829 is a number with 3 digits.
What are the multiples of 829?
The multiples of 829 are all integers evenly divisible by 829, that is all numbers such that the remainder of the division by 829 is zero. There are infinitely many multiples of 829. The smallest multiples of 829 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 829 too, since 0 × 829 = 0
- 829: indeed, 829 is a multiple of itself, since 829 is evenly divisible by 829 (we have 829 / 829 = 1, so the remainder of this division is indeed zero)
- 1 658: indeed, 1 658 = 829 × 2
- 2 487: indeed, 2 487 = 829 × 3
- 3 316: indeed, 3 316 = 829 × 4
- 4 145: indeed, 4 145 = 829 × 5
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 829). 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 28.792). 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.