What are the divisors of 3056?

1, 2, 4, 8, 16, 191, 382, 764, 1528, 3056

There is a total of 10 positive divisors.
The sum of these divisors is 5952.
The arithmetic mean is 595.2.

8 even divisors

2, 4, 8, 16, 382, 764, 1528, 3056

2 odd divisors

1, 191

How to compute the divisors of 3056?

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 3056 by each of the numbers from 1 to 3056 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)

3056 / 1 = 3056 (the remainder is 0, so 1 is a divisor of 3056)
3056 / 2 = 1528 (the remainder is 0, so 2 is a divisor of 3056)
3056 / 3 = 1018.6666666667 (the remainder is 2, so 3 is not a divisor of 3056)
...
3056 / 3055 = 1.0003273322422 (the remainder is 1, so 3055 is not a divisor of 3056)
3056 / 3056 = 1 (the remainder is 0, so 3056 is a divisor of 3056)

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 3056 (i.e. 55.281099844341). 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 $\frac{N}{d} = D$ )

3056 / 1 = 3056 (the remainder is 0, so 1 and 3056 are divisors of 3056)
3056 / 2 = 1528 (the remainder is 0, so 2 and 1528 are divisors of 3056)
3056 / 3 = 1018.6666666667 (the remainder is 2, so 3 is not a divisor of 3056)
...
3056 / 54 = 56.592592592593 (the remainder is 32, so 54 is not a divisor of 3056)
3056 / 55 = 55.563636363636 (the remainder is 31, so 55 is not a divisor of 3056)