What are the divisors of 4715?

1, 5, 23, 41, 115, 205, 943, 4715

There is a total of 8 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 756.

8 odd divisors

1, 5, 23, 41, 115, 205, 943, 4715

How to compute the divisors of 4715?

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 4715 by each of the numbers from 1 to 4715 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)

4715 / 1 = 4715 (the remainder is 0, so 1 is a divisor of 4715)
4715 / 2 = 2357.5 (the remainder is 1, so 2 is not a divisor of 4715)
4715 / 3 = 1571.6666666667 (the remainder is 2, so 3 is not a divisor of 4715)
...
4715 / 4714 = 1.0002121340687 (the remainder is 1, so 4714 is not a divisor of 4715)
4715 / 4715 = 1 (the remainder is 0, so 4715 is a divisor of 4715)

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 4715 (i.e. 68.665857600412). 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 $\frac{N}{d} = D$ )

4715 / 1 = 4715 (the remainder is 0, so 1 and 4715 are divisors of 4715)
4715 / 2 = 2357.5 (the remainder is 1, so 2 is not a divisor of 4715)
4715 / 3 = 1571.6666666667 (the remainder is 2, so 3 is not a divisor of 4715)
...
4715 / 67 = 70.373134328358 (the remainder is 25, so 67 is not a divisor of 4715)
4715 / 68 = 69.338235294118 (the remainder is 23, so 68 is not a divisor of 4715)