What are the divisors of 9112?

1, 2, 4, 8, 17, 34, 67, 68, 134, 136, 268, 536, 1139, 2278, 4556, 9112

There is a total of 16 positive divisors.
The sum of these divisors is 18360.
The arithmetic mean is 1147.5.

12 even divisors

2, 4, 8, 34, 68, 134, 136, 268, 536, 2278, 4556, 9112

4 odd divisors

1, 17, 67, 1139

How to compute the divisors of 9112?

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 9112 by each of the numbers from 1 to 9112 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)

9112 / 1 = 9112 (the remainder is 0, so 1 is a divisor of 9112)
9112 / 2 = 4556 (the remainder is 0, so 2 is a divisor of 9112)
9112 / 3 = 3037.3333333333 (the remainder is 1, so 3 is not a divisor of 9112)
...
9112 / 9111 = 1.0001097574361 (the remainder is 1, so 9111 is not a divisor of 9112)
9112 / 9112 = 1 (the remainder is 0, so 9112 is a divisor of 9112)

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 9112 (i.e. 95.456796510254). 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 $\frac{N}{d} = D$ )

9112 / 1 = 9112 (the remainder is 0, so 1 and 9112 are divisors of 9112)
9112 / 2 = 4556 (the remainder is 0, so 2 and 4556 are divisors of 9112)
9112 / 3 = 3037.3333333333 (the remainder is 1, so 3 is not a divisor of 9112)
...
9112 / 94 = 96.936170212766 (the remainder is 88, so 94 is not a divisor of 9112)
9112 / 95 = 95.915789473684 (the remainder is 87, so 95 is not a divisor of 9112)