What are the divisors of 845?

1, 5, 13, 65, 169, 845

There is a total of 6 positive divisors.
The sum of these divisors is 1098.
The arithmetic mean is 183.

6 odd divisors

1, 5, 13, 65, 169, 845

How to compute the divisors of 845?

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 845 by each of the numbers from 1 to 845 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)

845 / 1 = 845 (the remainder is 0, so 1 is a divisor of 845)
845 / 2 = 422.5 (the remainder is 1, so 2 is not a divisor of 845)
845 / 3 = 281.66666666667 (the remainder is 2, so 3 is not a divisor of 845)
...
845 / 844 = 1.0011848341232 (the remainder is 1, so 844 is not a divisor of 845)
845 / 845 = 1 (the remainder is 0, so 845 is a divisor of 845)

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 845 (i.e. 29.068883707497). 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 $\frac{N}{d} = D$ )

845 / 1 = 845 (the remainder is 0, so 1 and 845 are divisors of 845)
845 / 2 = 422.5 (the remainder is 1, so 2 is not a divisor of 845)
845 / 3 = 281.66666666667 (the remainder is 2, so 3 is not a divisor of 845)
...
845 / 28 = 30.178571428571 (the remainder is 5, so 28 is not a divisor of 845)
845 / 29 = 29.137931034483 (the remainder is 4, so 29 is not a divisor of 845)