What are the divisors of 9170?

1, 2, 5, 7, 10, 14, 35, 70, 131, 262, 655, 917, 1310, 1834, 4585, 9170

There is a total of 16 positive divisors.
The sum of these divisors is 19008.
The arithmetic mean is 1188.

8 even divisors

2, 10, 14, 70, 262, 1310, 1834, 9170

8 odd divisors

1, 5, 7, 35, 131, 655, 917, 4585

How to compute the divisors of 9170?

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 9170 by each of the numbers from 1 to 9170 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)

9170 / 1 = 9170 (the remainder is 0, so 1 is a divisor of 9170)
9170 / 2 = 4585 (the remainder is 0, so 2 is a divisor of 9170)
9170 / 3 = 3056.6666666667 (the remainder is 2, so 3 is not a divisor of 9170)
...
9170 / 9169 = 1.0001090631476 (the remainder is 1, so 9169 is not a divisor of 9170)
9170 / 9170 = 1 (the remainder is 0, so 9170 is a divisor of 9170)

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 9170 (i.e. 95.760116958993). 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 $\frac{N}{d} = D$ )

9170 / 1 = 9170 (the remainder is 0, so 1 and 9170 are divisors of 9170)
9170 / 2 = 4585 (the remainder is 0, so 2 and 4585 are divisors of 9170)
9170 / 3 = 3056.6666666667 (the remainder is 2, so 3 is not a divisor of 9170)
...
9170 / 94 = 97.553191489362 (the remainder is 52, so 94 is not a divisor of 9170)
9170 / 95 = 96.526315789474 (the remainder is 50, so 95 is not a divisor of 9170)