What are the divisors of 4356?

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 121, 132, 198, 242, 363, 396, 484, 726, 1089, 1452, 2178, 4356

There is a total of 27 positive divisors.
The sum of these divisors is 12103.
The arithmetic mean is 448.25925925926.

18 even divisors

2, 4, 6, 12, 18, 22, 36, 44, 66, 132, 198, 242, 396, 484, 726, 1452, 2178, 4356

9 odd divisors

1, 3, 9, 11, 33, 99, 121, 363, 1089

How to compute the divisors of 4356?

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 4356 by each of the numbers from 1 to 4356 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)

4356 / 1 = 4356 (the remainder is 0, so 1 is a divisor of 4356)
4356 / 2 = 2178 (the remainder is 0, so 2 is a divisor of 4356)
4356 / 3 = 1452 (the remainder is 0, so 3 is a divisor of 4356)
...
4356 / 4355 = 1.0002296211251 (the remainder is 1, so 4355 is not a divisor of 4356)
4356 / 4356 = 1 (the remainder is 0, so 4356 is a divisor of 4356)

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 4356 (i.e. 66). 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 $\frac{N}{d} = D$ )

4356 / 1 = 4356 (the remainder is 0, so 1 and 4356 are divisors of 4356)
4356 / 2 = 2178 (the remainder is 0, so 2 and 2178 are divisors of 4356)
4356 / 3 = 1452 (the remainder is 0, so 3 and 1452 are divisors of 4356)
...
4356 / 65 = 67.015384615385 (the remainder is 1, so 65 is not a divisor of 4356)
4356 / 66 = 66 (the remainder is 0, so 66 and 66 are divisors of 4356)