What are the divisors of 5292?

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 49, 54, 63, 84, 98, 108, 126, 147, 189, 196, 252, 294, 378, 441, 588, 756, 882, 1323, 1764, 2646, 5292

There is a total of 36 positive divisors.
The sum of these divisors is 15960.
The arithmetic mean is 443.33333333333.

24 even divisors

2, 4, 6, 12, 14, 18, 28, 36, 42, 54, 84, 98, 108, 126, 196, 252, 294, 378, 588, 756, 882, 1764, 2646, 5292

12 odd divisors

1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323

How to compute the divisors of 5292?

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 5292 by each of the numbers from 1 to 5292 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)

5292 / 1 = 5292 (the remainder is 0, so 1 is a divisor of 5292)
5292 / 2 = 2646 (the remainder is 0, so 2 is a divisor of 5292)
5292 / 3 = 1764 (the remainder is 0, so 3 is a divisor of 5292)
...
5292 / 5291 = 1.000189000189 (the remainder is 1, so 5291 is not a divisor of 5292)
5292 / 5292 = 1 (the remainder is 0, so 5292 is a divisor of 5292)

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 5292 (i.e. 72.746133917893). 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 $\frac{N}{d} = D$ )

5292 / 1 = 5292 (the remainder is 0, so 1 and 5292 are divisors of 5292)
5292 / 2 = 2646 (the remainder is 0, so 2 and 2646 are divisors of 5292)
5292 / 3 = 1764 (the remainder is 0, so 3 and 1764 are divisors of 5292)
...
5292 / 71 = 74.535211267606 (the remainder is 38, so 71 is not a divisor of 5292)
5292 / 72 = 73.5 (the remainder is 36, so 72 is not a divisor of 5292)