What are the divisors of 4711?

1, 7, 673, 4711

There is a total of 4 positive divisors.
The sum of these divisors is 5392.
The arithmetic mean is 1348.

4 odd divisors

1, 7, 673, 4711

How to compute the divisors of 4711?

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 4711 by each of the numbers from 1 to 4711 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)

4711 / 1 = 4711 (the remainder is 0, so 1 is a divisor of 4711)
4711 / 2 = 2355.5 (the remainder is 1, so 2 is not a divisor of 4711)
4711 / 3 = 1570.3333333333 (the remainder is 1, so 3 is not a divisor of 4711)
...
4711 / 4710 = 1.0002123142251 (the remainder is 1, so 4710 is not a divisor of 4711)
4711 / 4711 = 1 (the remainder is 0, so 4711 is a divisor of 4711)

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 4711 (i.e. 68.636724863589). 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 $\frac{N}{d} = D$ )

4711 / 1 = 4711 (the remainder is 0, so 1 and 4711 are divisors of 4711)
4711 / 2 = 2355.5 (the remainder is 1, so 2 is not a divisor of 4711)
4711 / 3 = 1570.3333333333 (the remainder is 1, so 3 is not a divisor of 4711)
...
4711 / 67 = 70.313432835821 (the remainder is 21, so 67 is not a divisor of 4711)
4711 / 68 = 69.279411764706 (the remainder is 19, so 68 is not a divisor of 4711)