What are the divisors of 4727?

1, 29, 163, 4727

There is a total of 4 positive divisors.
The sum of these divisors is 4920.
The arithmetic mean is 1230.

4 odd divisors

1, 29, 163, 4727

How to compute the divisors of 4727?

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 4727 by each of the numbers from 1 to 4727 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)

4727 / 1 = 4727 (the remainder is 0, so 1 is a divisor of 4727)
4727 / 2 = 2363.5 (the remainder is 1, so 2 is not a divisor of 4727)
4727 / 3 = 1575.6666666667 (the remainder is 2, so 3 is not a divisor of 4727)
...
4727 / 4726 = 1.0002115954295 (the remainder is 1, so 4726 is not a divisor of 4727)
4727 / 4727 = 1 (the remainder is 0, so 4727 is a divisor of 4727)

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 4727 (i.e. 68.753181744556). 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 $\frac{N}{d} = D$ )

4727 / 1 = 4727 (the remainder is 0, so 1 and 4727 are divisors of 4727)
4727 / 2 = 2363.5 (the remainder is 1, so 2 is not a divisor of 4727)
4727 / 3 = 1575.6666666667 (the remainder is 2, so 3 is not a divisor of 4727)
...
4727 / 67 = 70.55223880597 (the remainder is 37, so 67 is not a divisor of 4727)
4727 / 68 = 69.514705882353 (the remainder is 35, so 68 is not a divisor of 4727)