What are the divisors of 5171?

1, 5171

There is a total of 2 positive divisors.
The sum of these divisors is 5172.
The arithmetic mean is 2586.

2 odd divisors

1, 5171

How to compute the divisors of 5171?

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 5171 by each of the numbers from 1 to 5171 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)

5171 / 1 = 5171 (the remainder is 0, so 1 is a divisor of 5171)
5171 / 2 = 2585.5 (the remainder is 1, so 2 is not a divisor of 5171)
5171 / 3 = 1723.6666666667 (the remainder is 2, so 3 is not a divisor of 5171)
...
5171 / 5170 = 1.0001934235977 (the remainder is 1, so 5170 is not a divisor of 5171)
5171 / 5171 = 1 (the remainder is 0, so 5171 is a divisor of 5171)

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 5171 (i.e. 71.909665553387). 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 $\frac{N}{d} = D$ )

5171 / 1 = 5171 (the remainder is 0, so 1 and 5171 are divisors of 5171)
5171 / 2 = 2585.5 (the remainder is 1, so 2 is not a divisor of 5171)
5171 / 3 = 1723.6666666667 (the remainder is 2, so 3 is not a divisor of 5171)
...
5171 / 70 = 73.871428571429 (the remainder is 61, so 70 is not a divisor of 5171)
5171 / 71 = 72.830985915493 (the remainder is 59, so 71 is not a divisor of 5171)