What are the divisors of 4845?

1, 3, 5, 15, 17, 19, 51, 57, 85, 95, 255, 285, 323, 969, 1615, 4845

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

16 odd divisors

1, 3, 5, 15, 17, 19, 51, 57, 85, 95, 255, 285, 323, 969, 1615, 4845

How to compute the divisors of 4845?

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 4845 by each of the numbers from 1 to 4845 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)

4845 / 1 = 4845 (the remainder is 0, so 1 is a divisor of 4845)
4845 / 2 = 2422.5 (the remainder is 1, so 2 is not a divisor of 4845)
4845 / 3 = 1615 (the remainder is 0, so 3 is a divisor of 4845)
...
4845 / 4844 = 1.0002064409579 (the remainder is 1, so 4844 is not a divisor of 4845)
4845 / 4845 = 1 (the remainder is 0, so 4845 is a divisor of 4845)

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 4845 (i.e. 69.606034221179). 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 $\frac{N}{d} = D$ )

4845 / 1 = 4845 (the remainder is 0, so 1 and 4845 are divisors of 4845)
4845 / 2 = 2422.5 (the remainder is 1, so 2 is not a divisor of 4845)
4845 / 3 = 1615 (the remainder is 0, so 3 and 1615 are divisors of 4845)
...
4845 / 68 = 71.25 (the remainder is 17, so 68 is not a divisor of 4845)
4845 / 69 = 70.217391304348 (the remainder is 15, so 69 is not a divisor of 4845)