Is 9931 a prime number? What are the divisors of 9931?

## Is 9931 a prime number?

Yes, 9931 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 9931, the only two divisors are 1 and 9931. Therefore 9931 is a prime number.

As a consequence, 9931 is only a multiple of 1 and 9931.

Since 9931 is a prime number, 9931 is also a deficient number, that is to say 9931 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 9931 without 9931 itself (that is 1, by definition!).

## Parity of 9931

9931 is an odd number, because it is not evenly divisible by 2.

## Is 9931 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 9931 is about 99.654.

Thus, the square root of 9931 is not an integer, and therefore 9931 is not a square number.

Anyway, 9931 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 9931?

The square of a number (here 9931) is the result of the product of this number (9931) by itself (i.e., 9931 × 9931); the square of 9931 is sometimes called "raising 9931 to the power 2", or "9931 squared".

The square of 9931 is 98 624 761 because 9931 × 9931 = 99312 = 98 624 761.

As a consequence, 9931 is the square root of 98 624 761.

## Number of digits of 9931

9931 is a number with 4 digits.

## What are the multiples of 9931?

The multiples of 9931 are all integers evenly divisible by 9931, that is all numbers such that the remainder of the division by 9931 is zero. There are infinitely many multiples of 9931. The smallest multiples of 9931 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 9931 too, since 0 × 9931 = 0
• 9931: indeed, 9931 is a multiple of itself, since 9931 is evenly divisible by 9931 (we have 9931 / 9931 = 1, so the remainder of this division is indeed zero)
• 19 862: indeed, 19 862 = 9931 × 2
• 29 793: indeed, 29 793 = 9931 × 3
• 39 724: indeed, 39 724 = 9931 × 4
• 49 655: indeed, 49 655 = 9931 × 5
• etc.

## Nearest numbers from 9931

Find out whether some integer is a prime number