It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 10 338 is not a prime number.
For example, 10 338 can be divided by 2: 10 338 / 2 = 5 169.
For 10 338 to be a prime number, it would have been required that 10 338 has only two divisors, i.e., itself and 1.
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10 338 is an even number, because it is evenly divisible by 2: 10 338 / 2 = 5 169.
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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 10 338 is about 101.676.
Thus, the square root of 10 338 is not an integer, and therefore 10 338 is not a square number.
The square of a number (here 10 338) is the result of the product of this number (10 338) by itself (i.e., 10 338 × 10 338); the square of 10 338 is sometimes called "raising 10 338 to the power 2", or "10 338 squared".
The square of 10 338 is 106 874 244 because 10 338 × 10 338 = 10 3382 = 106 874 244.
As a consequence, 10 338 is the square root of 106 874 244.
The multiples of 10 338 are all integers evenly divisible by 10 338, that is all numbers such that the remainder of the division by 10 338 is zero. There are infinitely many multiples of 10 338. The smallest multiples of 10 338 are: