It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 10 823 is not a prime number.
For example, 10 823 can be divided by 79: 10 823 / 79 = 137.
For 10 823 to be a prime number, it would have been required that 10 823 has only two divisors, i.e., itself and 1.
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10 823 is an odd number, because it is not evenly divisible by 2.
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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 10 823 is about 104.034.
Thus, the square root of 10 823 is not an integer, and therefore 10 823 is not a square number.
The square of a number (here 10 823) is the result of the product of this number (10 823) by itself (i.e., 10 823 × 10 823); the square of 10 823 is sometimes called "raising 10 823 to the power 2", or "10 823 squared".
The square of 10 823 is 117 137 329 because 10 823 × 10 823 = 10 8232 = 117 137 329.
As a consequence, 10 823 is the square root of 117 137 329.
The multiples of 10 823 are all integers evenly divisible by 10 823, that is all numbers such that the remainder of the division by 10 823 is zero. There are infinitely many multiples of 10 823. The smallest multiples of 10 823 are: