What are the divisors of 3112?

1, 2, 4, 8, 389, 778, 1556, 3112

There is a total of 8 positive divisors.
The sum of these divisors is 5850.
The arithmetic mean is 731.25.

6 even divisors

2, 4, 8, 778, 1556, 3112

2 odd divisors

1, 389

How to compute the divisors of 3112?

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 3112 by each of the numbers from 1 to 3112 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)

3112 / 1 = 3112 (the remainder is 0, so 1 is a divisor of 3112)
3112 / 2 = 1556 (the remainder is 0, so 2 is a divisor of 3112)
3112 / 3 = 1037.3333333333 (the remainder is 1, so 3 is not a divisor of 3112)
...
3112 / 3111 = 1.0003214400514 (the remainder is 1, so 3111 is not a divisor of 3112)
3112 / 3112 = 1 (the remainder is 0, so 3112 is a divisor of 3112)

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 3112 (i.e. 55.785302723925). 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 $\frac{N}{d} = D$ )

3112 / 1 = 3112 (the remainder is 0, so 1 and 3112 are divisors of 3112)
3112 / 2 = 1556 (the remainder is 0, so 2 and 1556 are divisors of 3112)
3112 / 3 = 1037.3333333333 (the remainder is 1, so 3 is not a divisor of 3112)
...
3112 / 54 = 57.62962962963 (the remainder is 34, so 54 is not a divisor of 3112)
3112 / 55 = 56.581818181818 (the remainder is 32, so 55 is not a divisor of 3112)