What are the divisors of 1304?

1, 2, 4, 8, 163, 326, 652, 1304

There is a total of 8 positive divisors.
The sum of these divisors is 2460.
The arithmetic mean is 307.5.

6 even divisors

2, 4, 8, 326, 652, 1304

2 odd divisors

1, 163

How to compute the divisors of 1304?

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 1304 by each of the numbers from 1 to 1304 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)

1304 / 1 = 1304 (the remainder is 0, so 1 is a divisor of 1304)
1304 / 2 = 652 (the remainder is 0, so 2 is a divisor of 1304)
1304 / 3 = 434.66666666667 (the remainder is 2, so 3 is not a divisor of 1304)
...
1304 / 1303 = 1.0007674597084 (the remainder is 1, so 1303 is not a divisor of 1304)
1304 / 1304 = 1 (the remainder is 0, so 1304 is a divisor of 1304)

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 1304 (i.e. 36.110940170536). 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 $\frac{N}{d} = D$ )

1304 / 1 = 1304 (the remainder is 0, so 1 and 1304 are divisors of 1304)
1304 / 2 = 652 (the remainder is 0, so 2 and 652 are divisors of 1304)
1304 / 3 = 434.66666666667 (the remainder is 2, so 3 is not a divisor of 1304)
...
1304 / 35 = 37.257142857143 (the remainder is 9, so 35 is not a divisor of 1304)
1304 / 36 = 36.222222222222 (the remainder is 8, so 36 is not a divisor of 1304)