What are the divisors of 5544?

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 18, 21, 22, 24, 28, 33, 36, 42, 44, 56, 63, 66, 72, 77, 84, 88, 99, 126, 132, 154, 168, 198, 231, 252, 264, 308, 396, 462, 504, 616, 693, 792, 924, 1386, 1848, 2772, 5544

There is a total of 48 positive divisors.
The sum of these divisors is 18720.
The arithmetic mean is 390.

36 even divisors

2, 4, 6, 8, 12, 14, 18, 22, 24, 28, 36, 42, 44, 56, 66, 72, 84, 88, 126, 132, 154, 168, 198, 252, 264, 308, 396, 462, 504, 616, 792, 924, 1386, 1848, 2772, 5544

12 odd divisors

1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693

How to compute the divisors of 5544?

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 5544 by each of the numbers from 1 to 5544 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)

5544 / 1 = 5544 (the remainder is 0, so 1 is a divisor of 5544)
5544 / 2 = 2772 (the remainder is 0, so 2 is a divisor of 5544)
5544 / 3 = 1848 (the remainder is 0, so 3 is a divisor of 5544)
...
5544 / 5543 = 1.0001804077215 (the remainder is 1, so 5543 is not a divisor of 5544)
5544 / 5544 = 1 (the remainder is 0, so 5544 is a divisor of 5544)

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 5544 (i.e. 74.458041875945). 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 $\frac{N}{d} = D$ )

5544 / 1 = 5544 (the remainder is 0, so 1 and 5544 are divisors of 5544)
5544 / 2 = 2772 (the remainder is 0, so 2 and 2772 are divisors of 5544)
5544 / 3 = 1848 (the remainder is 0, so 3 and 1848 are divisors of 5544)
...
5544 / 73 = 75.945205479452 (the remainder is 69, so 73 is not a divisor of 5544)
5544 / 74 = 74.918918918919 (the remainder is 68, so 74 is not a divisor of 5544)