What are the divisors of 9196?

1, 2, 4, 11, 19, 22, 38, 44, 76, 121, 209, 242, 418, 484, 836, 2299, 4598, 9196

There is a total of 18 positive divisors.
The sum of these divisors is 18620.
The arithmetic mean is 1034.4444444444.

12 even divisors

2, 4, 22, 38, 44, 76, 242, 418, 484, 836, 4598, 9196

6 odd divisors

1, 11, 19, 121, 209, 2299

How to compute the divisors of 9196?

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 9196 by each of the numbers from 1 to 9196 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)

9196 / 1 = 9196 (the remainder is 0, so 1 is a divisor of 9196)
9196 / 2 = 4598 (the remainder is 0, so 2 is a divisor of 9196)
9196 / 3 = 3065.3333333333 (the remainder is 1, so 3 is not a divisor of 9196)
...
9196 / 9195 = 1.000108754758 (the remainder is 1, so 9195 is not a divisor of 9196)
9196 / 9196 = 1 (the remainder is 0, so 9196 is a divisor of 9196)

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 9196 (i.e. 95.895776757895). 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 $\frac{N}{d} = D$ )

9196 / 1 = 9196 (the remainder is 0, so 1 and 9196 are divisors of 9196)
9196 / 2 = 4598 (the remainder is 0, so 2 and 4598 are divisors of 9196)
9196 / 3 = 3065.3333333333 (the remainder is 1, so 3 is not a divisor of 9196)
...
9196 / 94 = 97.829787234043 (the remainder is 78, so 94 is not a divisor of 9196)
9196 / 95 = 96.8 (the remainder is 76, so 95 is not a divisor of 9196)