What are the divisors of 1088?

1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 136, 272, 544, 1088

There is a total of 14 positive divisors.
The sum of these divisors is 2286.
The arithmetic mean is 163.28571428571.

12 even divisors

2, 4, 8, 16, 32, 34, 64, 68, 136, 272, 544, 1088

2 odd divisors

1, 17

How to compute the divisors of 1088?

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 1088 by each of the numbers from 1 to 1088 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)

1088 / 1 = 1088 (the remainder is 0, so 1 is a divisor of 1088)
1088 / 2 = 544 (the remainder is 0, so 2 is a divisor of 1088)
1088 / 3 = 362.66666666667 (the remainder is 2, so 3 is not a divisor of 1088)
...
1088 / 1087 = 1.0009199632015 (the remainder is 1, so 1087 is not a divisor of 1088)
1088 / 1088 = 1 (the remainder is 0, so 1088 is a divisor of 1088)

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 1088 (i.e. 32.984845004941). 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 $\frac{N}{d} = D$ )

1088 / 1 = 1088 (the remainder is 0, so 1 and 1088 are divisors of 1088)
1088 / 2 = 544 (the remainder is 0, so 2 and 544 are divisors of 1088)
1088 / 3 = 362.66666666667 (the remainder is 2, so 3 is not a divisor of 1088)
...
1088 / 31 = 35.096774193548 (the remainder is 3, so 31 is not a divisor of 1088)
1088 / 32 = 34 (the remainder is 0, so 32 and 34 are divisors of 1088)