What are the divisors of 1124?

1, 2, 4, 281, 562, 1124

There is a total of 6 positive divisors.
The sum of these divisors is 1974.
The arithmetic mean is 329.

4 even divisors

2, 4, 562, 1124

2 odd divisors

1, 281

How to compute the divisors of 1124?

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 1124 by each of the numbers from 1 to 1124 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)

1124 / 1 = 1124 (the remainder is 0, so 1 is a divisor of 1124)
1124 / 2 = 562 (the remainder is 0, so 2 is a divisor of 1124)
1124 / 3 = 374.66666666667 (the remainder is 2, so 3 is not a divisor of 1124)
...
1124 / 1123 = 1.0008904719501 (the remainder is 1, so 1123 is not a divisor of 1124)
1124 / 1124 = 1 (the remainder is 0, so 1124 is a divisor of 1124)

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 1124 (i.e. 33.52610922848). 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 $\frac{N}{d} = D$ )

1124 / 1 = 1124 (the remainder is 0, so 1 and 1124 are divisors of 1124)
1124 / 2 = 562 (the remainder is 0, so 2 and 562 are divisors of 1124)
1124 / 3 = 374.66666666667 (the remainder is 2, so 3 is not a divisor of 1124)
...
1124 / 32 = 35.125 (the remainder is 4, so 32 is not a divisor of 1124)
1124 / 33 = 34.060606060606 (the remainder is 2, so 33 is not a divisor of 1124)