What are the divisors of 4735?

1, 5, 947, 4735

There is a total of 4 positive divisors.
The sum of these divisors is 5688.
The arithmetic mean is 1422.

4 odd divisors

1, 5, 947, 4735

How to compute the divisors of 4735?

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 4735 by each of the numbers from 1 to 4735 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)

4735 / 1 = 4735 (the remainder is 0, so 1 is a divisor of 4735)
4735 / 2 = 2367.5 (the remainder is 1, so 2 is not a divisor of 4735)
4735 / 3 = 1578.3333333333 (the remainder is 1, so 3 is not a divisor of 4735)
...
4735 / 4734 = 1.0002112378538 (the remainder is 1, so 4734 is not a divisor of 4735)
4735 / 4735 = 1 (the remainder is 0, so 4735 is a divisor of 4735)

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 4735 (i.e. 68.811336275355). 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 $\frac{N}{d} = D$ )

4735 / 1 = 4735 (the remainder is 0, so 1 and 4735 are divisors of 4735)
4735 / 2 = 2367.5 (the remainder is 1, so 2 is not a divisor of 4735)
4735 / 3 = 1578.3333333333 (the remainder is 1, so 3 is not a divisor of 4735)
...
4735 / 67 = 70.671641791045 (the remainder is 45, so 67 is not a divisor of 4735)
4735 / 68 = 69.632352941176 (the remainder is 43, so 68 is not a divisor of 4735)