What are the divisors of 4692?

1, 2, 3, 4, 6, 12, 17, 23, 34, 46, 51, 68, 69, 92, 102, 138, 204, 276, 391, 782, 1173, 1564, 2346, 4692

There is a total of 24 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 504.

16 even divisors

2, 4, 6, 12, 34, 46, 68, 92, 102, 138, 204, 276, 782, 1564, 2346, 4692

8 odd divisors

1, 3, 17, 23, 51, 69, 391, 1173

How to compute the divisors of 4692?

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 4692 by each of the numbers from 1 to 4692 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)

4692 / 1 = 4692 (the remainder is 0, so 1 is a divisor of 4692)
4692 / 2 = 2346 (the remainder is 0, so 2 is a divisor of 4692)
4692 / 3 = 1564 (the remainder is 0, so 3 is a divisor of 4692)
...
4692 / 4691 = 1.0002131741633 (the remainder is 1, so 4691 is not a divisor of 4692)
4692 / 4692 = 1 (the remainder is 0, so 4692 is a divisor of 4692)

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 4692 (i.e. 68.498175158175). 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 $\frac{N}{d} = D$ )

4692 / 1 = 4692 (the remainder is 0, so 1 and 4692 are divisors of 4692)
4692 / 2 = 2346 (the remainder is 0, so 2 and 2346 are divisors of 4692)
4692 / 3 = 1564 (the remainder is 0, so 3 and 1564 are divisors of 4692)
...
4692 / 67 = 70.029850746269 (the remainder is 2, so 67 is not a divisor of 4692)
4692 / 68 = 69 (the remainder is 0, so 68 and 69 are divisors of 4692)