What are the divisors of 5235?

1, 3, 5, 15, 349, 1047, 1745, 5235

There is a total of 8 positive divisors.
The sum of these divisors is 8400.
The arithmetic mean is 1050.

8 odd divisors

1, 3, 5, 15, 349, 1047, 1745, 5235

How to compute the divisors of 5235?

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 5235 by each of the numbers from 1 to 5235 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)

5235 / 1 = 5235 (the remainder is 0, so 1 is a divisor of 5235)
5235 / 2 = 2617.5 (the remainder is 1, so 2 is not a divisor of 5235)
5235 / 3 = 1745 (the remainder is 0, so 3 is a divisor of 5235)
...
5235 / 5234 = 1.0001910584639 (the remainder is 1, so 5234 is not a divisor of 5235)
5235 / 5235 = 1 (the remainder is 0, so 5235 is a divisor of 5235)

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 5235 (i.e. 72.353299855639). 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 $\frac{N}{d} = D$ )

5235 / 1 = 5235 (the remainder is 0, so 1 and 5235 are divisors of 5235)
5235 / 2 = 2617.5 (the remainder is 1, so 2 is not a divisor of 5235)
5235 / 3 = 1745 (the remainder is 0, so 3 and 1745 are divisors of 5235)
...
5235 / 71 = 73.732394366197 (the remainder is 52, so 71 is not a divisor of 5235)
5235 / 72 = 72.708333333333 (the remainder is 51, so 72 is not a divisor of 5235)