What are the divisors of 5013?

1, 3, 9, 557, 1671, 5013

There is a total of 6 positive divisors.
The sum of these divisors is 7254.
The arithmetic mean is 1209.

6 odd divisors

1, 3, 9, 557, 1671, 5013

How to compute the divisors of 5013?

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 5013 by each of the numbers from 1 to 5013 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)

5013 / 1 = 5013 (the remainder is 0, so 1 is a divisor of 5013)
5013 / 2 = 2506.5 (the remainder is 1, so 2 is not a divisor of 5013)
5013 / 3 = 1671 (the remainder is 0, so 3 is a divisor of 5013)
...
5013 / 5012 = 1.0001995211492 (the remainder is 1, so 5012 is not a divisor of 5013)
5013 / 5013 = 1 (the remainder is 0, so 5013 is a divisor of 5013)

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 5013 (i.e. 70.802542327236). 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 $\frac{N}{d} = D$ )

5013 / 1 = 5013 (the remainder is 0, so 1 and 5013 are divisors of 5013)
5013 / 2 = 2506.5 (the remainder is 1, so 2 is not a divisor of 5013)
5013 / 3 = 1671 (the remainder is 0, so 3 and 1671 are divisors of 5013)
...
5013 / 69 = 72.652173913043 (the remainder is 45, so 69 is not a divisor of 5013)
5013 / 70 = 71.614285714286 (the remainder is 43, so 70 is not a divisor of 5013)