What are the divisors of 4615?

1, 5, 13, 65, 71, 355, 923, 4615

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, 13, 65, 71, 355, 923, 4615

How to compute the divisors of 4615?

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 4615 by each of the numbers from 1 to 4615 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)

4615 / 1 = 4615 (the remainder is 0, so 1 is a divisor of 4615)
4615 / 2 = 2307.5 (the remainder is 1, so 2 is not a divisor of 4615)
4615 / 3 = 1538.3333333333 (the remainder is 1, so 3 is not a divisor of 4615)
...
4615 / 4614 = 1.0002167316862 (the remainder is 1, so 4614 is not a divisor of 4615)
4615 / 4615 = 1 (the remainder is 0, so 4615 is a divisor of 4615)

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 4615 (i.e. 67.933791297115). 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 $\frac{N}{d} = D$ )

4615 / 1 = 4615 (the remainder is 0, so 1 and 4615 are divisors of 4615)
4615 / 2 = 2307.5 (the remainder is 1, so 2 is not a divisor of 4615)
4615 / 3 = 1538.3333333333 (the remainder is 1, so 3 is not a divisor of 4615)
...
4615 / 66 = 69.924242424242 (the remainder is 61, so 66 is not a divisor of 4615)
4615 / 67 = 68.880597014925 (the remainder is 59, so 67 is not a divisor of 4615)