What are the divisors of 5267?

1, 23, 229, 5267

There is a total of 4 positive divisors.
The sum of these divisors is 5520.
The arithmetic mean is 1380.

4 odd divisors

1, 23, 229, 5267

How to compute the divisors of 5267?

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 5267 by each of the numbers from 1 to 5267 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)

5267 / 1 = 5267 (the remainder is 0, so 1 is a divisor of 5267)
5267 / 2 = 2633.5 (the remainder is 1, so 2 is not a divisor of 5267)
5267 / 3 = 1755.6666666667 (the remainder is 2, so 3 is not a divisor of 5267)
...
5267 / 5266 = 1.0001898974554 (the remainder is 1, so 5266 is not a divisor of 5267)
5267 / 5267 = 1 (the remainder is 0, so 5267 is a divisor of 5267)

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 5267 (i.e. 72.574100063315). 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 $\frac{N}{d} = D$ )

5267 / 1 = 5267 (the remainder is 0, so 1 and 5267 are divisors of 5267)
5267 / 2 = 2633.5 (the remainder is 1, so 2 is not a divisor of 5267)
5267 / 3 = 1755.6666666667 (the remainder is 2, so 3 is not a divisor of 5267)
...
5267 / 71 = 74.183098591549 (the remainder is 13, so 71 is not a divisor of 5267)
5267 / 72 = 73.152777777778 (the remainder is 11, so 72 is not a divisor of 5267)