What are the divisors of 3013?

1, 23, 131, 3013

There is a total of 4 positive divisors.
The sum of these divisors is 3168.
The arithmetic mean is 792.

4 odd divisors

1, 23, 131, 3013

How to compute the divisors of 3013?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3013 by each of the numbers from 1 to 3013 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3013 / 1 = 3013 (the remainder is 0, so 1 is a divisor of 3013)
3013 / 2 = 1506.5 (the remainder is 1, so 2 is not a divisor of 3013)
3013 / 3 = 1004.3333333333 (the remainder is 1, so 3 is not a divisor of 3013)
...
3013 / 3012 = 1.0003320053121 (the remainder is 1, so 3012 is not a divisor of 3013)
3013 / 3013 = 1 (the remainder is 0, so 3013 is a divisor of 3013)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3013 (i.e. 54.890800686454). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3013 / 1 = 3013 (the remainder is 0, so 1 and 3013 are divisors of 3013)
3013 / 2 = 1506.5 (the remainder is 1, so 2 is not a divisor of 3013)
3013 / 3 = 1004.3333333333 (the remainder is 1, so 3 is not a divisor of 3013)
...
3013 / 53 = 56.849056603774 (the remainder is 45, so 53 is not a divisor of 3013)
3013 / 54 = 55.796296296296 (the remainder is 43, so 54 is not a divisor of 3013)