What are the divisors of 1108?

1, 2, 4, 277, 554, 1108

There is a total of 6 positive divisors.
The sum of these divisors is 1946.
The arithmetic mean is 324.33333333333.

4 even divisors

2, 4, 554, 1108

2 odd divisors

1, 277

How to compute the divisors of 1108?

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 1108 by each of the numbers from 1 to 1108 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)

1108 / 1 = 1108 (the remainder is 0, so 1 is a divisor of 1108)
1108 / 2 = 554 (the remainder is 0, so 2 is a divisor of 1108)
1108 / 3 = 369.33333333333 (the remainder is 1, so 3 is not a divisor of 1108)
...
1108 / 1107 = 1.0009033423668 (the remainder is 1, so 1107 is not a divisor of 1108)
1108 / 1108 = 1 (the remainder is 0, so 1108 is a divisor of 1108)

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 1108 (i.e. 33.286633954186). 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 $\frac{N}{d} = D$ )

1108 / 1 = 1108 (the remainder is 0, so 1 and 1108 are divisors of 1108)
1108 / 2 = 554 (the remainder is 0, so 2 and 554 are divisors of 1108)
1108 / 3 = 369.33333333333 (the remainder is 1, so 3 is not a divisor of 1108)
...
1108 / 32 = 34.625 (the remainder is 20, so 32 is not a divisor of 1108)
1108 / 33 = 33.575757575758 (the remainder is 19, so 33 is not a divisor of 1108)