What are the divisors of 9145?

1, 5, 31, 59, 155, 295, 1829, 9145

There is a total of 8 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 1440.

8 odd divisors

1, 5, 31, 59, 155, 295, 1829, 9145

How to compute the divisors of 9145?

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 9145 by each of the numbers from 1 to 9145 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)

9145 / 1 = 9145 (the remainder is 0, so 1 is a divisor of 9145)
9145 / 2 = 4572.5 (the remainder is 1, so 2 is not a divisor of 9145)
9145 / 3 = 3048.3333333333 (the remainder is 1, so 3 is not a divisor of 9145)
...
9145 / 9144 = 1.0001093613298 (the remainder is 1, so 9144 is not a divisor of 9145)
9145 / 9145 = 1 (the remainder is 0, so 9145 is a divisor of 9145)

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 9145 (i.e. 95.629493358482). 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 $\frac{N}{d} = D$ )

9145 / 1 = 9145 (the remainder is 0, so 1 and 9145 are divisors of 9145)
9145 / 2 = 4572.5 (the remainder is 1, so 2 is not a divisor of 9145)
9145 / 3 = 3048.3333333333 (the remainder is 1, so 3 is not a divisor of 9145)
...
9145 / 94 = 97.287234042553 (the remainder is 27, so 94 is not a divisor of 9145)
9145 / 95 = 96.263157894737 (the remainder is 25, so 95 is not a divisor of 9145)