What are the divisors of 5275?

1, 5, 25, 211, 1055, 5275

There is a total of 6 positive divisors.
The sum of these divisors is 6572.
The arithmetic mean is 1095.3333333333.

6 odd divisors

1, 5, 25, 211, 1055, 5275

How to compute the divisors of 5275?

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 5275 by each of the numbers from 1 to 5275 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)

5275 / 1 = 5275 (the remainder is 0, so 1 is a divisor of 5275)
5275 / 2 = 2637.5 (the remainder is 1, so 2 is not a divisor of 5275)
5275 / 3 = 1758.3333333333 (the remainder is 1, so 3 is not a divisor of 5275)
...
5275 / 5274 = 1.0001896094046 (the remainder is 1, so 5274 is not a divisor of 5275)
5275 / 5275 = 1 (the remainder is 0, so 5275 is a divisor of 5275)

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 5275 (i.e. 72.62919523167). 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 $\frac{N}{d} = D$ )

5275 / 1 = 5275 (the remainder is 0, so 1 and 5275 are divisors of 5275)
5275 / 2 = 2637.5 (the remainder is 1, so 2 is not a divisor of 5275)
5275 / 3 = 1758.3333333333 (the remainder is 1, so 3 is not a divisor of 5275)
...
5275 / 71 = 74.295774647887 (the remainder is 21, so 71 is not a divisor of 5275)
5275 / 72 = 73.263888888889 (the remainder is 19, so 72 is not a divisor of 5275)