Is 9901 a prime number? What are the divisors of 9901?

## Is 9901 a prime number?

Yes, 9901 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 9901, the only two divisors are 1 and 9901. Therefore 9901 is a prime number.

As a consequence, 9901 is only a multiple of 1 and 9901.

Since 9901 is a prime number, 9901 is also a deficient number, that is to say 9901 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 9901 without 9901 itself (that is 1, by definition!).

## Parity of 9901

9901 is an odd number, because it is not evenly divisible by 2.

## Is 9901 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 9901 is about 99.504.

Thus, the square root of 9901 is not an integer, and therefore 9901 is not a square number.

Anyway, 9901 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 9901?

The square of a number (here 9901) is the result of the product of this number (9901) by itself (i.e., 9901 × 9901); the square of 9901 is sometimes called "raising 9901 to the power 2", or "9901 squared".

The square of 9901 is 98 029 801 because 9901 × 9901 = 99012 = 98 029 801.

As a consequence, 9901 is the square root of 98 029 801.

## Number of digits of 9901

9901 is a number with 4 digits.

## What are the multiples of 9901?

The multiples of 9901 are all integers evenly divisible by 9901, that is all numbers such that the remainder of the division by 9901 is zero. There are infinitely many multiples of 9901. The smallest multiples of 9901 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 9901 too, since 0 × 9901 = 0
• 9901: indeed, 9901 is a multiple of itself, since 9901 is evenly divisible by 9901 (we have 9901 / 9901 = 1, so the remainder of this division is indeed zero)
• 19 802: indeed, 19 802 = 9901 × 2
• 29 703: indeed, 29 703 = 9901 × 3
• 39 604: indeed, 39 604 = 9901 × 4
• 49 505: indeed, 49 505 = 9901 × 5
• etc.

## Nearest numbers from 9901

Find out whether some integer is a prime number