Is 7537 a prime number? What are the divisors of 7537?

## Is 7537 a prime number?

Yes, 7537 is a prime number.

Indeed, the definition of a prime numbers is to have only two distinct positive divisors, 1 and itself. A number is a divisor of another number when the remainder of Euclid’s division of the second one by the first one is zero. Concerning the number 7537, the only two divisors are 1 and 7537. Therefore 7537 is a prime number.

As a consequence, 7537 is only a multiple of 1 and 7537.

Since 7537 is a prime number, 7537 is also a deficient number, that is to say 7537 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 7537 without 7537 itself (that is 1, by definition!).

## Parity of 7537

7537 is an odd number, because it is not evenly divisible by 2.

## Is 7537 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 7537 is about 86.816.

Thus, the square root of 7537 is not an integer, and therefore 7537 is not a square number.

Anyway, 7537 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 7537?

The square of a number (here 7537) is the result of the product of this number (7537) by itself (i.e., 7537 × 7537); the square of 7537 is sometimes called "raising 7537 to the power 2", or "7537 squared".

The square of 7537 is 56 806 369 because 7537 × 7537 = 75372 = 56 806 369.

As a consequence, 7537 is the square root of 56 806 369.

## Number of digits of 7537

7537 is a number with 4 digits.

## What are the multiples of 7537?

The multiples of 7537 are all integers evenly divisible by 7537, that is all numbers such that the remainder of the division by 7537 is zero. There are infinitely many multiples of 7537. The smallest multiples of 7537 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 7537 too, since 0 × 7537 = 0
• 7537: indeed, 7537 is a multiple of itself, since 7537 is evenly divisible by 7537 (we have 7537 / 7537 = 1, so the remainder of this division is indeed zero)
• 15 074: indeed, 15 074 = 7537 × 2
• 22 611: indeed, 22 611 = 7537 × 3
• 30 148: indeed, 30 148 = 7537 × 4
• 37 685: indeed, 37 685 = 7537 × 5
• etc.

## Nearest numbers from 7537

Find out whether some integer is a prime number