What are the divisors of 5652?

1, 2, 3, 4, 6, 9, 12, 18, 36, 157, 314, 471, 628, 942, 1413, 1884, 2826, 5652

There is a total of 18 positive divisors.
The sum of these divisors is 14378.
The arithmetic mean is 798.77777777778.

12 even divisors

2, 4, 6, 12, 18, 36, 314, 628, 942, 1884, 2826, 5652

6 odd divisors

1, 3, 9, 157, 471, 1413

How to compute the divisors of 5652?

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 5652 by each of the numbers from 1 to 5652 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)

5652 / 1 = 5652 (the remainder is 0, so 1 is a divisor of 5652)
5652 / 2 = 2826 (the remainder is 0, so 2 is a divisor of 5652)
5652 / 3 = 1884 (the remainder is 0, so 3 is a divisor of 5652)
...
5652 / 5651 = 1.0001769598301 (the remainder is 1, so 5651 is not a divisor of 5652)
5652 / 5652 = 1 (the remainder is 0, so 5652 is a divisor of 5652)

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 5652 (i.e. 75.17978451685). 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 $\frac{N}{d} = D$ )

5652 / 1 = 5652 (the remainder is 0, so 1 and 5652 are divisors of 5652)
5652 / 2 = 2826 (the remainder is 0, so 2 and 2826 are divisors of 5652)
5652 / 3 = 1884 (the remainder is 0, so 3 and 1884 are divisors of 5652)
...
5652 / 74 = 76.378378378378 (the remainder is 28, so 74 is not a divisor of 5652)
5652 / 75 = 75.36 (the remainder is 27, so 75 is not a divisor of 5652)