What are the divisors of 5081?

1, 5081

There is a total of 2 positive divisors.
The sum of these divisors is 5082.
The arithmetic mean is 2541.

2 odd divisors

1, 5081

How to compute the divisors of 5081?

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 5081 by each of the numbers from 1 to 5081 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)

5081 / 1 = 5081 (the remainder is 0, so 1 is a divisor of 5081)
5081 / 2 = 2540.5 (the remainder is 1, so 2 is not a divisor of 5081)
5081 / 3 = 1693.6666666667 (the remainder is 2, so 3 is not a divisor of 5081)
...
5081 / 5080 = 1.0001968503937 (the remainder is 1, so 5080 is not a divisor of 5081)
5081 / 5081 = 1 (the remainder is 0, so 5081 is a divisor of 5081)

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 5081 (i.e. 71.281133548787). 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 $\frac{N}{d} = D$ )

5081 / 1 = 5081 (the remainder is 0, so 1 and 5081 are divisors of 5081)
5081 / 2 = 2540.5 (the remainder is 1, so 2 is not a divisor of 5081)
5081 / 3 = 1693.6666666667 (the remainder is 2, so 3 is not a divisor of 5081)
...
5081 / 70 = 72.585714285714 (the remainder is 41, so 70 is not a divisor of 5081)
5081 / 71 = 71.56338028169 (the remainder is 40, so 71 is not a divisor of 5081)