What are the divisors of 3104?

1, 2, 4, 8, 16, 32, 97, 194, 388, 776, 1552, 3104

There is a total of 12 positive divisors.
The sum of these divisors is 6174.
The arithmetic mean is 514.5.

10 even divisors

2, 4, 8, 16, 32, 194, 388, 776, 1552, 3104

2 odd divisors

1, 97

How to compute the divisors of 3104?

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 3104 by each of the numbers from 1 to 3104 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)

3104 / 1 = 3104 (the remainder is 0, so 1 is a divisor of 3104)
3104 / 2 = 1552 (the remainder is 0, so 2 is a divisor of 3104)
3104 / 3 = 1034.6666666667 (the remainder is 2, so 3 is not a divisor of 3104)
...
3104 / 3103 = 1.0003222687722 (the remainder is 1, so 3103 is not a divisor of 3104)
3104 / 3104 = 1 (the remainder is 0, so 3104 is a divisor of 3104)

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 3104 (i.e. 55.713553108736). 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 $\frac{N}{d} = D$ )

3104 / 1 = 3104 (the remainder is 0, so 1 and 3104 are divisors of 3104)
3104 / 2 = 1552 (the remainder is 0, so 2 and 1552 are divisors of 3104)
3104 / 3 = 1034.6666666667 (the remainder is 2, so 3 is not a divisor of 3104)
...
3104 / 54 = 57.481481481481 (the remainder is 26, so 54 is not a divisor of 3104)
3104 / 55 = 56.436363636364 (the remainder is 24, so 55 is not a divisor of 3104)