Is 4003 a prime number? What are the divisors of 4003?

## Is 4003 a prime number?

Yes, 4003 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 4003, the only two divisors are 1 and 4003. Therefore 4003 is a prime number.

As a consequence, 4003 is only a multiple of 1 and 4003.

Since 4003 is a prime number, 4003 is also a deficient number, that is to say 4003 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 4003 without 4003 itself (that is 1, by definition!).

## Parity of 4003

4003 is an odd number, because it is not evenly divisible by 2.

## Is 4003 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 4003 is about 63.269.

Thus, the square root of 4003 is not an integer, and therefore 4003 is not a square number.

Anyway, 4003 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 4003?

The square of a number (here 4003) is the result of the product of this number (4003) by itself (i.e., 4003 × 4003); the square of 4003 is sometimes called "raising 4003 to the power 2", or "4003 squared".

The square of 4003 is 16 024 009 because 4003 × 4003 = 40032 = 16 024 009.

As a consequence, 4003 is the square root of 16 024 009.

## Number of digits of 4003

4003 is a number with 4 digits.

## What are the multiples of 4003?

The multiples of 4003 are all integers evenly divisible by 4003, that is all numbers such that the remainder of the division by 4003 is zero. There are infinitely many multiples of 4003. The smallest multiples of 4003 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 4003 too, since 0 × 4003 = 0
• 4003: indeed, 4003 is a multiple of itself, since 4003 is evenly divisible by 4003 (we have 4003 / 4003 = 1, so the remainder of this division is indeed zero)
• 8 006: indeed, 8 006 = 4003 × 2
• 12 009: indeed, 12 009 = 4003 × 3
• 16 012: indeed, 16 012 = 4003 × 4
• 20 015: indeed, 20 015 = 4003 × 5
• etc.

## Nearest numbers from 4003

Find out whether some integer is a prime number