What are the divisors of 5617?

1, 41, 137, 5617

There is a total of 4 positive divisors.
The sum of these divisors is 5796.
The arithmetic mean is 1449.

4 odd divisors

1, 41, 137, 5617

How to compute the divisors of 5617?

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 5617 by each of the numbers from 1 to 5617 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)

5617 / 1 = 5617 (the remainder is 0, so 1 is a divisor of 5617)
5617 / 2 = 2808.5 (the remainder is 1, so 2 is not a divisor of 5617)
5617 / 3 = 1872.3333333333 (the remainder is 1, so 3 is not a divisor of 5617)
...
5617 / 5616 = 1.0001780626781 (the remainder is 1, so 5616 is not a divisor of 5617)
5617 / 5617 = 1 (the remainder is 0, so 5617 is a divisor of 5617)

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 5617 (i.e. 74.946647690207). 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 $\frac{N}{d} = D$ )

5617 / 1 = 5617 (the remainder is 0, so 1 and 5617 are divisors of 5617)
5617 / 2 = 2808.5 (the remainder is 1, so 2 is not a divisor of 5617)
5617 / 3 = 1872.3333333333 (the remainder is 1, so 3 is not a divisor of 5617)
...
5617 / 73 = 76.945205479452 (the remainder is 69, so 73 is not a divisor of 5617)
5617 / 74 = 75.905405405405 (the remainder is 67, so 74 is not a divisor of 5617)