What are the divisors of 9154?

1, 2, 23, 46, 199, 398, 4577, 9154

There is a total of 8 positive divisors.
The sum of these divisors is 14400.
The arithmetic mean is 1800.

4 even divisors

2, 46, 398, 9154

4 odd divisors

1, 23, 199, 4577

How to compute the divisors of 9154?

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 9154 by each of the numbers from 1 to 9154 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)

9154 / 1 = 9154 (the remainder is 0, so 1 is a divisor of 9154)
9154 / 2 = 4577 (the remainder is 0, so 2 is a divisor of 9154)
9154 / 3 = 3051.3333333333 (the remainder is 1, so 3 is not a divisor of 9154)
...
9154 / 9153 = 1.0001092537966 (the remainder is 1, so 9153 is not a divisor of 9154)
9154 / 9154 = 1 (the remainder is 0, so 9154 is a divisor of 9154)

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 9154 (i.e. 95.67653839892). 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 $\frac{N}{d} = D$ )

9154 / 1 = 9154 (the remainder is 0, so 1 and 9154 are divisors of 9154)
9154 / 2 = 4577 (the remainder is 0, so 2 and 4577 are divisors of 9154)
9154 / 3 = 3051.3333333333 (the remainder is 1, so 3 is not a divisor of 9154)
...
9154 / 94 = 97.382978723404 (the remainder is 36, so 94 is not a divisor of 9154)
9154 / 95 = 96.357894736842 (the remainder is 34, so 95 is not a divisor of 9154)