What are the divisors of 1128?

1, 2, 3, 4, 6, 8, 12, 24, 47, 94, 141, 188, 282, 376, 564, 1128

There is a total of 16 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 180.

12 even divisors

2, 4, 6, 8, 12, 24, 94, 188, 282, 376, 564, 1128

4 odd divisors

1, 3, 47, 141

How to compute the divisors of 1128?

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 1128 by each of the numbers from 1 to 1128 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)

1128 / 1 = 1128 (the remainder is 0, so 1 is a divisor of 1128)
1128 / 2 = 564 (the remainder is 0, so 2 is a divisor of 1128)
1128 / 3 = 376 (the remainder is 0, so 3 is a divisor of 1128)
...
1128 / 1127 = 1.0008873114463 (the remainder is 1, so 1127 is not a divisor of 1128)
1128 / 1128 = 1 (the remainder is 0, so 1128 is a divisor of 1128)

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 1128 (i.e. 33.585711247493). 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 $\frac{N}{d} = D$ )

1128 / 1 = 1128 (the remainder is 0, so 1 and 1128 are divisors of 1128)
1128 / 2 = 564 (the remainder is 0, so 2 and 564 are divisors of 1128)
1128 / 3 = 376 (the remainder is 0, so 3 and 376 are divisors of 1128)
...
1128 / 32 = 35.25 (the remainder is 8, so 32 is not a divisor of 1128)
1128 / 33 = 34.181818181818 (the remainder is 6, so 33 is not a divisor of 1128)