What are the divisors of 6112?

1, 2, 4, 8, 16, 32, 191, 382, 764, 1528, 3056, 6112

There is a total of 12 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 1008.

10 even divisors

2, 4, 8, 16, 32, 382, 764, 1528, 3056, 6112

2 odd divisors

1, 191

How to compute the divisors of 6112?

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 6112 by each of the numbers from 1 to 6112 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)

6112 / 1 = 6112 (the remainder is 0, so 1 is a divisor of 6112)
6112 / 2 = 3056 (the remainder is 0, so 2 is a divisor of 6112)
6112 / 3 = 2037.3333333333 (the remainder is 1, so 3 is not a divisor of 6112)
...
6112 / 6111 = 1.0001636393389 (the remainder is 1, so 6111 is not a divisor of 6112)
6112 / 6112 = 1 (the remainder is 0, so 6112 is a divisor of 6112)

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 6112 (i.e. 78.179281142768). 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 $\frac{N}{d} = D$ )

6112 / 1 = 6112 (the remainder is 0, so 1 and 6112 are divisors of 6112)
6112 / 2 = 3056 (the remainder is 0, so 2 and 3056 are divisors of 6112)
6112 / 3 = 2037.3333333333 (the remainder is 1, so 3 is not a divisor of 6112)
...
6112 / 77 = 79.376623376623 (the remainder is 29, so 77 is not a divisor of 6112)
6112 / 78 = 78.358974358974 (the remainder is 28, so 78 is not a divisor of 6112)