What are the divisors of 4865?

1, 5, 7, 35, 139, 695, 973, 4865

There is a total of 8 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 840.

8 odd divisors

1, 5, 7, 35, 139, 695, 973, 4865

How to compute the divisors of 4865?

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 4865 by each of the numbers from 1 to 4865 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)

4865 / 1 = 4865 (the remainder is 0, so 1 is a divisor of 4865)
4865 / 2 = 2432.5 (the remainder is 1, so 2 is not a divisor of 4865)
4865 / 3 = 1621.6666666667 (the remainder is 2, so 3 is not a divisor of 4865)
...
4865 / 4864 = 1.0002055921053 (the remainder is 1, so 4864 is not a divisor of 4865)
4865 / 4865 = 1 (the remainder is 0, so 4865 is a divisor of 4865)

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 4865 (i.e. 69.749551969887). 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 $\frac{N}{d} = D$ )

4865 / 1 = 4865 (the remainder is 0, so 1 and 4865 are divisors of 4865)
4865 / 2 = 2432.5 (the remainder is 1, so 2 is not a divisor of 4865)
4865 / 3 = 1621.6666666667 (the remainder is 2, so 3 is not a divisor of 4865)
...
4865 / 68 = 71.544117647059 (the remainder is 37, so 68 is not a divisor of 4865)
4865 / 69 = 70.507246376812 (the remainder is 35, so 69 is not a divisor of 4865)