What are the divisors of 5675?

1, 5, 25, 227, 1135, 5675

There is a total of 6 positive divisors.
The sum of these divisors is 7068.
The arithmetic mean is 1178.

6 odd divisors

1, 5, 25, 227, 1135, 5675

How to compute the divisors of 5675?

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 5675 by each of the numbers from 1 to 5675 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)

5675 / 1 = 5675 (the remainder is 0, so 1 is a divisor of 5675)
5675 / 2 = 2837.5 (the remainder is 1, so 2 is not a divisor of 5675)
5675 / 3 = 1891.6666666667 (the remainder is 2, so 3 is not a divisor of 5675)
...
5675 / 5674 = 1.0001762425097 (the remainder is 1, so 5674 is not a divisor of 5675)
5675 / 5675 = 1 (the remainder is 0, so 5675 is a divisor of 5675)

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 5675 (i.e. 75.332595866597). 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 $\frac{N}{d} = D$ )

5675 / 1 = 5675 (the remainder is 0, so 1 and 5675 are divisors of 5675)
5675 / 2 = 2837.5 (the remainder is 1, so 2 is not a divisor of 5675)
5675 / 3 = 1891.6666666667 (the remainder is 2, so 3 is not a divisor of 5675)
...
5675 / 74 = 76.689189189189 (the remainder is 51, so 74 is not a divisor of 5675)
5675 / 75 = 75.666666666667 (the remainder is 50, so 75 is not a divisor of 5675)