It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 7 501 is not a prime number.
For example, 7 501 can be divided by 13: 7 501 / 13 = 577.
For 7 501 to be a prime number, it would have been required that 7 501 has only two divisors, i.e., itself and 1.
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7 501 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 7 501 is about 86.608.
Thus, the square root of 7 501 is not an integer, and therefore 7 501 is not a square number.
The square of a number (here 7 501) is the result of the product of this number (7 501) by itself (i.e., 7 501 × 7 501); the square of 7 501 is sometimes called "raising 7 501 to the power 2", or "7 501 squared".
The square of 7 501 is 56 265 001 because 7 501 × 7 501 = 7 5012 = 56 265 001.
As a consequence, 7 501 is the square root of 56 265 001.
The multiples of 7 501 are all integers evenly divisible by 7 501, that is all numbers such that the remainder of the division by 7 501 is zero. There are infinitely many multiples of 7 501. The smallest multiples of 7 501 are: