Is 9967 a prime number? What are the divisors of 9967?

## Is 9967 a prime number?

Yes, 9967 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 9967, the only two divisors are 1 and 9967. Therefore 9967 is a prime number.

As a consequence, 9967 is only a multiple of 1 and 9967.

Since 9967 is a prime number, 9967 is also a deficient number, that is to say 9967 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 9967 without 9967 itself (that is 1, by definition!).

## Parity of 9967

9967 is an odd number, because it is not evenly divisible by 2.

## Is 9967 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 9967 is about 99.835.

Thus, the square root of 9967 is not an integer, and therefore 9967 is not a square number.

Anyway, 9967 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 9967?

The square of a number (here 9967) is the result of the product of this number (9967) by itself (i.e., 9967 × 9967); the square of 9967 is sometimes called "raising 9967 to the power 2", or "9967 squared".

The square of 9967 is 99 341 089 because 9967 × 9967 = 99672 = 99 341 089.

As a consequence, 9967 is the square root of 99 341 089.

## Number of digits of 9967

9967 is a number with 4 digits.

## What are the multiples of 9967?

The multiples of 9967 are all integers evenly divisible by 9967, that is all numbers such that the remainder of the division by 9967 is zero. There are infinitely many multiples of 9967. The smallest multiples of 9967 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 9967 too, since 0 × 9967 = 0
• 9967: indeed, 9967 is a multiple of itself, since 9967 is evenly divisible by 9967 (we have 9967 / 9967 = 1, so the remainder of this division is indeed zero)
• 19 934: indeed, 19 934 = 9967 × 2
• 29 901: indeed, 29 901 = 9967 × 3
• 39 868: indeed, 39 868 = 9967 × 4
• 49 835: indeed, 49 835 = 9967 × 5
• etc.

## Nearest numbers from 9967

Find out whether some integer is a prime number