What are the divisors of 4705?

1, 5, 941, 4705

There is a total of 4 positive divisors.
The sum of these divisors is 5652.
The arithmetic mean is 1413.

4 odd divisors

1, 5, 941, 4705

How to compute the divisors of 4705?

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 4705 by each of the numbers from 1 to 4705 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)

4705 / 1 = 4705 (the remainder is 0, so 1 is a divisor of 4705)
4705 / 2 = 2352.5 (the remainder is 1, so 2 is not a divisor of 4705)
4705 / 3 = 1568.3333333333 (the remainder is 1, so 3 is not a divisor of 4705)
...
4705 / 4704 = 1.000212585034 (the remainder is 1, so 4704 is not a divisor of 4705)
4705 / 4705 = 1 (the remainder is 0, so 4705 is a divisor of 4705)

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 4705 (i.e. 68.59300255857). 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 $\frac{N}{d} = D$ )

4705 / 1 = 4705 (the remainder is 0, so 1 and 4705 are divisors of 4705)
4705 / 2 = 2352.5 (the remainder is 1, so 2 is not a divisor of 4705)
4705 / 3 = 1568.3333333333 (the remainder is 1, so 3 is not a divisor of 4705)
...
4705 / 67 = 70.223880597015 (the remainder is 15, so 67 is not a divisor of 4705)
4705 / 68 = 69.191176470588 (the remainder is 13, so 68 is not a divisor of 4705)