What are the divisors of 5575?

1, 5, 25, 223, 1115, 5575

There is a total of 6 positive divisors.
The sum of these divisors is 6944.
The arithmetic mean is 1157.3333333333.

6 odd divisors

1, 5, 25, 223, 1115, 5575

How to compute the divisors of 5575?

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 5575 by each of the numbers from 1 to 5575 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)

5575 / 1 = 5575 (the remainder is 0, so 1 is a divisor of 5575)
5575 / 2 = 2787.5 (the remainder is 1, so 2 is not a divisor of 5575)
5575 / 3 = 1858.3333333333 (the remainder is 1, so 3 is not a divisor of 5575)
...
5575 / 5574 = 1.0001794043775 (the remainder is 1, so 5574 is not a divisor of 5575)
5575 / 5575 = 1 (the remainder is 0, so 5575 is a divisor of 5575)

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 5575 (i.e. 74.66592261534). 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 $\frac{N}{d} = D$ )

5575 / 1 = 5575 (the remainder is 0, so 1 and 5575 are divisors of 5575)
5575 / 2 = 2787.5 (the remainder is 1, so 2 is not a divisor of 5575)
5575 / 3 = 1858.3333333333 (the remainder is 1, so 3 is not a divisor of 5575)
...
5575 / 73 = 76.369863013699 (the remainder is 27, so 73 is not a divisor of 5575)
5575 / 74 = 75.337837837838 (the remainder is 25, so 74 is not a divisor of 5575)