What are the divisors of 4734?

1, 2, 3, 6, 9, 18, 263, 526, 789, 1578, 2367, 4734

There is a total of 12 positive divisors.
The sum of these divisors is 10296.
The arithmetic mean is 858.

6 even divisors

2, 6, 18, 526, 1578, 4734

6 odd divisors

1, 3, 9, 263, 789, 2367

How to compute the divisors of 4734?

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 4734 by each of the numbers from 1 to 4734 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)

4734 / 1 = 4734 (the remainder is 0, so 1 is a divisor of 4734)
4734 / 2 = 2367 (the remainder is 0, so 2 is a divisor of 4734)
4734 / 3 = 1578 (the remainder is 0, so 3 is a divisor of 4734)
...
4734 / 4733 = 1.0002112824847 (the remainder is 1, so 4733 is not a divisor of 4734)
4734 / 4734 = 1 (the remainder is 0, so 4734 is a divisor of 4734)

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 4734 (i.e. 68.804069647078). 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 $\frac{N}{d} = D$ )

4734 / 1 = 4734 (the remainder is 0, so 1 and 4734 are divisors of 4734)
4734 / 2 = 2367 (the remainder is 0, so 2 and 2367 are divisors of 4734)
4734 / 3 = 1578 (the remainder is 0, so 3 and 1578 are divisors of 4734)
...
4734 / 67 = 70.65671641791 (the remainder is 44, so 67 is not a divisor of 4734)
4734 / 68 = 69.617647058824 (the remainder is 42, so 68 is not a divisor of 4734)