It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 53 513 is not a prime number.
For example, 53 513 can be divided by 59: 53 513 / 59 = 907.
For 53 513 to be a prime number, it would have been required that 53 513 has only two divisors, i.e., itself and 1.
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53 513 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 53 513 is about 231.329.
Thus, the square root of 53 513 is not an integer, and therefore 53 513 is not a square number.
The square of a number (here 53 513) is the result of the product of this number (53 513) by itself (i.e., 53 513 × 53 513); the square of 53 513 is sometimes called "raising 53 513 to the power 2", or "53 513 squared".
The square of 53 513 is 2 863 641 169 because 53 513 × 53 513 = 53 5132 = 2 863 641 169.
As a consequence, 53 513 is the square root of 2 863 641 169.
The multiples of 53 513 are all integers evenly divisible by 53 513, that is all numbers such that the remainder of the division by 53 513 is zero. There are infinitely many multiples of 53 513. The smallest multiples of 53 513 are: