What are the divisors of 5352?

1, 2, 3, 4, 6, 8, 12, 24, 223, 446, 669, 892, 1338, 1784, 2676, 5352

There is a total of 16 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 840.

12 even divisors

2, 4, 6, 8, 12, 24, 446, 892, 1338, 1784, 2676, 5352

4 odd divisors

1, 3, 223, 669

How to compute the divisors of 5352?

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 5352 by each of the numbers from 1 to 5352 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)

5352 / 1 = 5352 (the remainder is 0, so 1 is a divisor of 5352)
5352 / 2 = 2676 (the remainder is 0, so 2 is a divisor of 5352)
5352 / 3 = 1784 (the remainder is 0, so 3 is a divisor of 5352)
...
5352 / 5351 = 1.0001868809568 (the remainder is 1, so 5351 is not a divisor of 5352)
5352 / 5352 = 1 (the remainder is 0, so 5352 is a divisor of 5352)

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 5352 (i.e. 73.157364632688). 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 $\frac{N}{d} = D$ )

5352 / 1 = 5352 (the remainder is 0, so 1 and 5352 are divisors of 5352)
5352 / 2 = 2676 (the remainder is 0, so 2 and 2676 are divisors of 5352)
5352 / 3 = 1784 (the remainder is 0, so 3 and 1784 are divisors of 5352)
...
5352 / 72 = 74.333333333333 (the remainder is 24, so 72 is not a divisor of 5352)
5352 / 73 = 73.315068493151 (the remainder is 23, so 73 is not a divisor of 5352)