What are the divisors of 9106?

1, 2, 29, 58, 157, 314, 4553, 9106

There is a total of 8 positive divisors.
The sum of these divisors is 14220.
The arithmetic mean is 1777.5.

4 even divisors

2, 58, 314, 9106

4 odd divisors

1, 29, 157, 4553

How to compute the divisors of 9106?

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 9106 by each of the numbers from 1 to 9106 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)

9106 / 1 = 9106 (the remainder is 0, so 1 is a divisor of 9106)
9106 / 2 = 4553 (the remainder is 0, so 2 is a divisor of 9106)
9106 / 3 = 3035.3333333333 (the remainder is 1, so 3 is not a divisor of 9106)
...
9106 / 9105 = 1.0001098297639 (the remainder is 1, so 9105 is not a divisor of 9106)
9106 / 9106 = 1 (the remainder is 0, so 9106 is a divisor of 9106)

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 9106 (i.e. 95.425363504678). 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 $\frac{N}{d} = D$ )

9106 / 1 = 9106 (the remainder is 0, so 1 and 9106 are divisors of 9106)
9106 / 2 = 4553 (the remainder is 0, so 2 and 4553 are divisors of 9106)
9106 / 3 = 3035.3333333333 (the remainder is 1, so 3 is not a divisor of 9106)
...
9106 / 94 = 96.872340425532 (the remainder is 82, so 94 is not a divisor of 9106)
9106 / 95 = 95.852631578947 (the remainder is 81, so 95 is not a divisor of 9106)