What are the divisors of 4687?

1, 43, 109, 4687

There is a total of 4 positive divisors.
The sum of these divisors is 4840.
The arithmetic mean is 1210.

4 odd divisors

1, 43, 109, 4687

How to compute the divisors of 4687?

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 4687 by each of the numbers from 1 to 4687 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)

4687 / 1 = 4687 (the remainder is 0, so 1 is a divisor of 4687)
4687 / 2 = 2343.5 (the remainder is 1, so 2 is not a divisor of 4687)
4687 / 3 = 1562.3333333333 (the remainder is 1, so 3 is not a divisor of 4687)
...
4687 / 4686 = 1.0002134016219 (the remainder is 1, so 4686 is not a divisor of 4687)
4687 / 4687 = 1 (the remainder is 0, so 4687 is a divisor of 4687)

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 4687 (i.e. 68.461668107051). 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 $\frac{N}{d} = D$ )

4687 / 1 = 4687 (the remainder is 0, so 1 and 4687 are divisors of 4687)
4687 / 2 = 2343.5 (the remainder is 1, so 2 is not a divisor of 4687)
4687 / 3 = 1562.3333333333 (the remainder is 1, so 3 is not a divisor of 4687)
...
4687 / 67 = 69.955223880597 (the remainder is 64, so 67 is not a divisor of 4687)
4687 / 68 = 68.926470588235 (the remainder is 63, so 68 is not a divisor of 4687)