What are the divisors of 1312?

1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, 1312

There is a total of 12 positive divisors.
The sum of these divisors is 2646.
The arithmetic mean is 220.5.

10 even divisors

2, 4, 8, 16, 32, 82, 164, 328, 656, 1312

2 odd divisors

1, 41

How to compute the divisors of 1312?

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 1312 by each of the numbers from 1 to 1312 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)

1312 / 1 = 1312 (the remainder is 0, so 1 is a divisor of 1312)
1312 / 2 = 656 (the remainder is 0, so 2 is a divisor of 1312)
1312 / 3 = 437.33333333333 (the remainder is 1, so 3 is not a divisor of 1312)
...
1312 / 1311 = 1.0007627765065 (the remainder is 1, so 1311 is not a divisor of 1312)
1312 / 1312 = 1 (the remainder is 0, so 1312 is a divisor of 1312)

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 1312 (i.e. 36.22154055255). 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 $\frac{N}{d} = D$ )

1312 / 1 = 1312 (the remainder is 0, so 1 and 1312 are divisors of 1312)
1312 / 2 = 656 (the remainder is 0, so 2 and 656 are divisors of 1312)
1312 / 3 = 437.33333333333 (the remainder is 1, so 3 is not a divisor of 1312)
...
1312 / 35 = 37.485714285714 (the remainder is 17, so 35 is not a divisor of 1312)
1312 / 36 = 36.444444444444 (the remainder is 16, so 36 is not a divisor of 1312)