Is 10009 a prime number? What are the divisors of 10009?

## Is 10009 a prime number?

Yes, 10009 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 10009, the only two divisors are 1 and 10009. Therefore 10009 is a prime number.

As a consequence, 10009 is only a multiple of 1 and 10009.

Since 10009 is a prime number, 10009 is also a deficient number, that is to say 10009 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 10009 without 10009 itself (that is 1, by definition!).

## Parity of 10009

10009 is an odd number, because it is not evenly divisible by 2.

## Is 10009 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 10009 is about 100.045.

Thus, the square root of 10009 is not an integer, and therefore 10009 is not a square number.

Anyway, 10009 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 10009?

The square of a number (here 10009) is the result of the product of this number (10009) by itself (i.e., 10009 × 10009); the square of 10009 is sometimes called "raising 10009 to the power 2", or "10009 squared".

The square of 10009 is 100 180 081 because 10009 × 10009 = 100092 = 100 180 081.

As a consequence, 10009 is the square root of 100 180 081.

## Number of digits of 10009

10009 is a number with 5 digits.

## What are the multiples of 10009?

The multiples of 10009 are all integers evenly divisible by 10009, that is all numbers such that the remainder of the division by 10009 is zero. There are infinitely many multiples of 10009. The smallest multiples of 10009 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 10009 too, since 0 × 10009 = 0
• 10009: indeed, 10009 is a multiple of itself, since 10009 is evenly divisible by 10009 (we have 10009 / 10009 = 1, so the remainder of this division is indeed zero)
• 20 018: indeed, 20 018 = 10009 × 2
• 30 027: indeed, 30 027 = 10009 × 3
• 40 036: indeed, 40 036 = 10009 × 4
• 50 045: indeed, 50 045 = 10009 × 5
• etc.

## Nearest numbers from 10009

Find out whether some integer is a prime number