Is 4001 a prime number? What are the divisors of 4001?

## Is 4001 a prime number?

Yes, 4001 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 4001, the only two divisors are 1 and 4001. Therefore 4001 is a prime number.

As a consequence, 4001 is only a multiple of 1 and 4001.

Since 4001 is a prime number, 4001 is also a deficient number, that is to say 4001 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 4001 without 4001 itself (that is 1, by definition!).

## Parity of 4001

4001 is an odd number, because it is not evenly divisible by 2.

## Is 4001 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 4001 is about 63.253.

Thus, the square root of 4001 is not an integer, and therefore 4001 is not a square number.

Anyway, 4001 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 4001?

The square of a number (here 4001) is the result of the product of this number (4001) by itself (i.e., 4001 × 4001); the square of 4001 is sometimes called "raising 4001 to the power 2", or "4001 squared".

The square of 4001 is 16 008 001 because 4001 × 4001 = 40012 = 16 008 001.

As a consequence, 4001 is the square root of 16 008 001.

## Number of digits of 4001

4001 is a number with 4 digits.

## What are the multiples of 4001?

The multiples of 4001 are all integers evenly divisible by 4001, that is all numbers such that the remainder of the division by 4001 is zero. There are infinitely many multiples of 4001. The smallest multiples of 4001 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 4001 too, since 0 × 4001 = 0
• 4001: indeed, 4001 is a multiple of itself, since 4001 is evenly divisible by 4001 (we have 4001 / 4001 = 1, so the remainder of this division is indeed zero)
• 8 002: indeed, 8 002 = 4001 × 2
• 12 003: indeed, 12 003 = 4001 × 3
• 16 004: indeed, 16 004 = 4001 × 4
• 20 005: indeed, 20 005 = 4001 × 5
• etc.

## Nearest numbers from 4001

Find out whether some integer is a prime number