What are the divisors of 5071?

1, 11, 461, 5071

There is a total of 4 positive divisors.
The sum of these divisors is 5544.
The arithmetic mean is 1386.

4 odd divisors

1, 11, 461, 5071

How to compute the divisors of 5071?

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 5071 by each of the numbers from 1 to 5071 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)

5071 / 1 = 5071 (the remainder is 0, so 1 is a divisor of 5071)
5071 / 2 = 2535.5 (the remainder is 1, so 2 is not a divisor of 5071)
5071 / 3 = 1690.3333333333 (the remainder is 1, so 3 is not a divisor of 5071)
...
5071 / 5070 = 1.0001972386588 (the remainder is 1, so 5070 is not a divisor of 5071)
5071 / 5071 = 1 (the remainder is 0, so 5071 is a divisor of 5071)

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 5071 (i.e. 71.21095421352). 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 $\frac{N}{d} = D$ )

5071 / 1 = 5071 (the remainder is 0, so 1 and 5071 are divisors of 5071)
5071 / 2 = 2535.5 (the remainder is 1, so 2 is not a divisor of 5071)
5071 / 3 = 1690.3333333333 (the remainder is 1, so 3 is not a divisor of 5071)
...
5071 / 70 = 72.442857142857 (the remainder is 31, so 70 is not a divisor of 5071)
5071 / 71 = 71.422535211268 (the remainder is 30, so 71 is not a divisor of 5071)