What are the divisors of 4815?

1, 3, 5, 9, 15, 45, 107, 321, 535, 963, 1605, 4815

There is a total of 12 positive divisors.
The sum of these divisors is 8424.
The arithmetic mean is 702.

12 odd divisors

1, 3, 5, 9, 15, 45, 107, 321, 535, 963, 1605, 4815

How to compute the divisors of 4815?

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 4815 by each of the numbers from 1 to 4815 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)

4815 / 1 = 4815 (the remainder is 0, so 1 is a divisor of 4815)
4815 / 2 = 2407.5 (the remainder is 1, so 2 is not a divisor of 4815)
4815 / 3 = 1605 (the remainder is 0, so 3 is a divisor of 4815)
...
4815 / 4814 = 1.0002077274616 (the remainder is 1, so 4814 is not a divisor of 4815)
4815 / 4815 = 1 (the remainder is 0, so 4815 is a divisor of 4815)

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 4815 (i.e. 69.390201037322). 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 $\frac{N}{d} = D$ )

4815 / 1 = 4815 (the remainder is 0, so 1 and 4815 are divisors of 4815)
4815 / 2 = 2407.5 (the remainder is 1, so 2 is not a divisor of 4815)
4815 / 3 = 1605 (the remainder is 0, so 3 and 1605 are divisors of 4815)
...
4815 / 68 = 70.808823529412 (the remainder is 55, so 68 is not a divisor of 4815)
4815 / 69 = 69.782608695652 (the remainder is 54, so 69 is not a divisor of 4815)