What are the divisors of 4698?

1, 2, 3, 6, 9, 18, 27, 29, 54, 58, 81, 87, 162, 174, 261, 522, 783, 1566, 2349, 4698

There is a total of 20 positive divisors.
The sum of these divisors is 10890.
The arithmetic mean is 544.5.

10 even divisors

2, 6, 18, 54, 58, 162, 174, 522, 1566, 4698

10 odd divisors

1, 3, 9, 27, 29, 81, 87, 261, 783, 2349

How to compute the divisors of 4698?

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 4698 by each of the numbers from 1 to 4698 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)

4698 / 1 = 4698 (the remainder is 0, so 1 is a divisor of 4698)
4698 / 2 = 2349 (the remainder is 0, so 2 is a divisor of 4698)
4698 / 3 = 1566 (the remainder is 0, so 3 is a divisor of 4698)
...
4698 / 4697 = 1.0002129018522 (the remainder is 1, so 4697 is not a divisor of 4698)
4698 / 4698 = 1 (the remainder is 0, so 4698 is a divisor of 4698)

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 4698 (i.e. 68.541957952775). 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 $\frac{N}{d} = D$ )

4698 / 1 = 4698 (the remainder is 0, so 1 and 4698 are divisors of 4698)
4698 / 2 = 2349 (the remainder is 0, so 2 and 2349 are divisors of 4698)
4698 / 3 = 1566 (the remainder is 0, so 3 and 1566 are divisors of 4698)
...
4698 / 67 = 70.119402985075 (the remainder is 8, so 67 is not a divisor of 4698)
4698 / 68 = 69.088235294118 (the remainder is 6, so 68 is not a divisor of 4698)