What are the divisors of 4733?

1, 4733

There is a total of 2 positive divisors.
The sum of these divisors is 4734.
The arithmetic mean is 2367.

2 odd divisors

1, 4733

How to compute the divisors of 4733?

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 4733 by each of the numbers from 1 to 4733 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)

4733 / 1 = 4733 (the remainder is 0, so 1 is a divisor of 4733)
4733 / 2 = 2366.5 (the remainder is 1, so 2 is not a divisor of 4733)
4733 / 3 = 1577.6666666667 (the remainder is 2, so 3 is not a divisor of 4733)
...
4733 / 4732 = 1.0002113271344 (the remainder is 1, so 4732 is not a divisor of 4733)
4733 / 4733 = 1 (the remainder is 0, so 4733 is a divisor of 4733)

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 4733 (i.e. 68.796802251267). 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 $\frac{N}{d} = D$ )

4733 / 1 = 4733 (the remainder is 0, so 1 and 4733 are divisors of 4733)
4733 / 2 = 2366.5 (the remainder is 1, so 2 is not a divisor of 4733)
4733 / 3 = 1577.6666666667 (the remainder is 2, so 3 is not a divisor of 4733)
...
4733 / 67 = 70.641791044776 (the remainder is 43, so 67 is not a divisor of 4733)
4733 / 68 = 69.602941176471 (the remainder is 41, so 68 is not a divisor of 4733)