What are the divisors of 1328?

1, 2, 4, 8, 16, 83, 166, 332, 664, 1328

There is a total of 10 positive divisors.
The sum of these divisors is 2604.
The arithmetic mean is 260.4.

8 even divisors

2, 4, 8, 16, 166, 332, 664, 1328

2 odd divisors

1, 83

How to compute the divisors of 1328?

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 1328 by each of the numbers from 1 to 1328 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)

1328 / 1 = 1328 (the remainder is 0, so 1 is a divisor of 1328)
1328 / 2 = 664 (the remainder is 0, so 2 is a divisor of 1328)
1328 / 3 = 442.66666666667 (the remainder is 2, so 3 is not a divisor of 1328)
...
1328 / 1327 = 1.0007535795026 (the remainder is 1, so 1327 is not a divisor of 1328)
1328 / 1328 = 1 (the remainder is 0, so 1328 is a divisor of 1328)

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 1328 (i.e. 36.441734316577). 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 $\frac{N}{d} = D$ )

1328 / 1 = 1328 (the remainder is 0, so 1 and 1328 are divisors of 1328)
1328 / 2 = 664 (the remainder is 0, so 2 and 664 are divisors of 1328)
1328 / 3 = 442.66666666667 (the remainder is 2, so 3 is not a divisor of 1328)
...
1328 / 35 = 37.942857142857 (the remainder is 33, so 35 is not a divisor of 1328)
1328 / 36 = 36.888888888889 (the remainder is 32, so 36 is not a divisor of 1328)