Is 4013 a prime number? What are the divisors of 4013?

## Is 4013 a prime number?

Yes, 4013 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 4013, the only two divisors are 1 and 4013. Therefore 4013 is a prime number.

As a consequence, 4013 is only a multiple of 1 and 4013.

Since 4013 is a prime number, 4013 is also a deficient number, that is to say 4013 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 4013 without 4013 itself (that is 1, by definition!).

## Parity of 4013

4013 is an odd number, because it is not evenly divisible by 2.

## Is 4013 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 4013 is about 63.348.

Thus, the square root of 4013 is not an integer, and therefore 4013 is not a square number.

Anyway, 4013 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 4013?

The square of a number (here 4013) is the result of the product of this number (4013) by itself (i.e., 4013 × 4013); the square of 4013 is sometimes called "raising 4013 to the power 2", or "4013 squared".

The square of 4013 is 16 104 169 because 4013 × 4013 = 40132 = 16 104 169.

As a consequence, 4013 is the square root of 16 104 169.

## Number of digits of 4013

4013 is a number with 4 digits.

## What are the multiples of 4013?

The multiples of 4013 are all integers evenly divisible by 4013, that is all numbers such that the remainder of the division by 4013 is zero. There are infinitely many multiples of 4013. The smallest multiples of 4013 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 4013 too, since 0 × 4013 = 0
• 4013: indeed, 4013 is a multiple of itself, since 4013 is evenly divisible by 4013 (we have 4013 / 4013 = 1, so the remainder of this division is indeed zero)
• 8 026: indeed, 8 026 = 4013 × 2
• 12 039: indeed, 12 039 = 4013 × 3
• 16 052: indeed, 16 052 = 4013 × 4
• 20 065: indeed, 20 065 = 4013 × 5
• etc.

## Nearest numbers from 4013

Find out whether some integer is a prime number