Is 3001 a prime number? What are the divisors of 3001?

## Is 3001 a prime number?

Yes, 3001 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 3001, the only two divisors are 1 and 3001. Therefore 3001 is a prime number.

As a consequence, 3001 is only a multiple of 1 and 3001.

Since 3001 is a prime number, 3001 is also a deficient number, that is to say 3001 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 3001 without 3001 itself (that is 1, by definition!).

## Parity of 3001

3001 is an odd number, because it is not evenly divisible by 2.

## Is 3001 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 3001 is about 54.781.

Thus, the square root of 3001 is not an integer, and therefore 3001 is not a square number.

Anyway, 3001 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 3001?

The square of a number (here 3001) is the result of the product of this number (3001) by itself (i.e., 3001 × 3001); the square of 3001 is sometimes called "raising 3001 to the power 2", or "3001 squared".

The square of 3001 is 9 006 001 because 3001 × 3001 = 30012 = 9 006 001.

As a consequence, 3001 is the square root of 9 006 001.

## Number of digits of 3001

3001 is a number with 4 digits.

## What are the multiples of 3001?

The multiples of 3001 are all integers evenly divisible by 3001, that is all numbers such that the remainder of the division by 3001 is zero. There are infinitely many multiples of 3001. The smallest multiples of 3001 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 3001 too, since 0 × 3001 = 0
• 3001: indeed, 3001 is a multiple of itself, since 3001 is evenly divisible by 3001 (we have 3001 / 3001 = 1, so the remainder of this division is indeed zero)
• 6 002: indeed, 6 002 = 3001 × 2
• 9 003: indeed, 9 003 = 3001 × 3
• 12 004: indeed, 12 004 = 3001 × 4
• 15 005: indeed, 15 005 = 3001 × 5
• etc.

## Nearest numbers from 3001

Find out whether some integer is a prime number