What are the divisors of 4707?

1, 3, 9, 523, 1569, 4707

There is a total of 6 positive divisors.
The sum of these divisors is 6812.
The arithmetic mean is 1135.3333333333.

6 odd divisors

1, 3, 9, 523, 1569, 4707

How to compute the divisors of 4707?

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 4707 by each of the numbers from 1 to 4707 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)

4707 / 1 = 4707 (the remainder is 0, so 1 is a divisor of 4707)
4707 / 2 = 2353.5 (the remainder is 1, so 2 is not a divisor of 4707)
4707 / 3 = 1569 (the remainder is 0, so 3 is a divisor of 4707)
...
4707 / 4706 = 1.0002124946876 (the remainder is 1, so 4706 is not a divisor of 4707)
4707 / 4707 = 1 (the remainder is 0, so 4707 is a divisor of 4707)

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 4707 (i.e. 68.607579756176). 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 $\frac{N}{d} = D$ )

4707 / 1 = 4707 (the remainder is 0, so 1 and 4707 are divisors of 4707)
4707 / 2 = 2353.5 (the remainder is 1, so 2 is not a divisor of 4707)
4707 / 3 = 1569 (the remainder is 0, so 3 and 1569 are divisors of 4707)
...
4707 / 67 = 70.253731343284 (the remainder is 17, so 67 is not a divisor of 4707)
4707 / 68 = 69.220588235294 (the remainder is 15, so 68 is not a divisor of 4707)