What are the divisors of 1547?

1, 7, 13, 17, 91, 119, 221, 1547

There is a total of 8 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 252.

8 odd divisors

1, 7, 13, 17, 91, 119, 221, 1547

How to compute the divisors of 1547?

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 1547 by each of the numbers from 1 to 1547 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)

1547 / 1 = 1547 (the remainder is 0, so 1 is a divisor of 1547)
1547 / 2 = 773.5 (the remainder is 1, so 2 is not a divisor of 1547)
1547 / 3 = 515.66666666667 (the remainder is 2, so 3 is not a divisor of 1547)
...
1547 / 1546 = 1.0006468305304 (the remainder is 1, so 1546 is not a divisor of 1547)
1547 / 1547 = 1 (the remainder is 0, so 1547 is a divisor of 1547)

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 1547 (i.e. 39.331920878594). 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 $\frac{N}{d} = D$ )

1547 / 1 = 1547 (the remainder is 0, so 1 and 1547 are divisors of 1547)
1547 / 2 = 773.5 (the remainder is 1, so 2 is not a divisor of 1547)
1547 / 3 = 515.66666666667 (the remainder is 2, so 3 is not a divisor of 1547)
...
1547 / 38 = 40.710526315789 (the remainder is 27, so 38 is not a divisor of 1547)
1547 / 39 = 39.666666666667 (the remainder is 26, so 39 is not a divisor of 1547)