What are the divisors of 9169?

1, 53, 173, 9169

There is a total of 4 positive divisors.
The sum of these divisors is 9396.
The arithmetic mean is 2349.

4 odd divisors

1, 53, 173, 9169

How to compute the divisors of 9169?

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 9169 by each of the numbers from 1 to 9169 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)

9169 / 1 = 9169 (the remainder is 0, so 1 is a divisor of 9169)
9169 / 2 = 4584.5 (the remainder is 1, so 2 is not a divisor of 9169)
9169 / 3 = 3056.3333333333 (the remainder is 1, so 3 is not a divisor of 9169)
...
9169 / 9168 = 1.0001090750436 (the remainder is 1, so 9168 is not a divisor of 9169)
9169 / 9169 = 1 (the remainder is 0, so 9169 is a divisor of 9169)

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 9169 (i.e. 95.754895436213). 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 $\frac{N}{d} = D$ )

9169 / 1 = 9169 (the remainder is 0, so 1 and 9169 are divisors of 9169)
9169 / 2 = 4584.5 (the remainder is 1, so 2 is not a divisor of 9169)
9169 / 3 = 3056.3333333333 (the remainder is 1, so 3 is not a divisor of 9169)
...
9169 / 94 = 97.542553191489 (the remainder is 51, so 94 is not a divisor of 9169)
9169 / 95 = 96.515789473684 (the remainder is 49, so 95 is not a divisor of 9169)