What are the divisors of 7104?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 37, 48, 64, 74, 96, 111, 148, 192, 222, 296, 444, 592, 888, 1184, 1776, 2368, 3552, 7104

There is a total of 28 positive divisors.
The sum of these divisors is 19304.
The arithmetic mean is 689.42857142857.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 74, 96, 148, 192, 222, 296, 444, 592, 888, 1184, 1776, 2368, 3552, 7104

4 odd divisors

1, 3, 37, 111

How to compute the divisors of 7104?

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 7104 by each of the numbers from 1 to 7104 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)

7104 / 1 = 7104 (the remainder is 0, so 1 is a divisor of 7104)
7104 / 2 = 3552 (the remainder is 0, so 2 is a divisor of 7104)
7104 / 3 = 2368 (the remainder is 0, so 3 is a divisor of 7104)
...
7104 / 7103 = 1.0001407855836 (the remainder is 1, so 7103 is not a divisor of 7104)
7104 / 7104 = 1 (the remainder is 0, so 7104 is a divisor of 7104)

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 7104 (i.e. 84.285230022822). 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 $\frac{N}{d} = D$ )

7104 / 1 = 7104 (the remainder is 0, so 1 and 7104 are divisors of 7104)
7104 / 2 = 3552 (the remainder is 0, so 2 and 3552 are divisors of 7104)
7104 / 3 = 2368 (the remainder is 0, so 3 and 2368 are divisors of 7104)
...
7104 / 83 = 85.590361445783 (the remainder is 49, so 83 is not a divisor of 7104)
7104 / 84 = 84.571428571429 (the remainder is 48, so 84 is not a divisor of 7104)