What are the divisors of 1288?

1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 92, 161, 184, 322, 644, 1288

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, 8, 14, 28, 46, 56, 92, 184, 322, 644, 1288

4 odd divisors

1, 7, 23, 161

How to compute the divisors of 1288?

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 1288 by each of the numbers from 1 to 1288 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)

1288 / 1 = 1288 (the remainder is 0, so 1 is a divisor of 1288)
1288 / 2 = 644 (the remainder is 0, so 2 is a divisor of 1288)
1288 / 3 = 429.33333333333 (the remainder is 1, so 3 is not a divisor of 1288)
...
1288 / 1287 = 1.000777000777 (the remainder is 1, so 1287 is not a divisor of 1288)
1288 / 1288 = 1 (the remainder is 0, so 1288 is a divisor of 1288)

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 1288 (i.e. 35.888716889853). 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 $\frac{N}{d} = D$ )

1288 / 1 = 1288 (the remainder is 0, so 1 and 1288 are divisors of 1288)
1288 / 2 = 644 (the remainder is 0, so 2 and 644 are divisors of 1288)
1288 / 3 = 429.33333333333 (the remainder is 1, so 3 is not a divisor of 1288)
...
1288 / 34 = 37.882352941176 (the remainder is 30, so 34 is not a divisor of 1288)
1288 / 35 = 36.8 (the remainder is 28, so 35 is not a divisor of 1288)