What are the divisors of 9157?

1, 9157

There is a total of 2 positive divisors.
The sum of these divisors is 9158.
The arithmetic mean is 4579.

2 odd divisors

1, 9157

How to compute the divisors of 9157?

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 9157 by each of the numbers from 1 to 9157 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)

9157 / 1 = 9157 (the remainder is 0, so 1 is a divisor of 9157)
9157 / 2 = 4578.5 (the remainder is 1, so 2 is not a divisor of 9157)
9157 / 3 = 3052.3333333333 (the remainder is 1, so 3 is not a divisor of 9157)
...
9157 / 9156 = 1.0001092179991 (the remainder is 1, so 9156 is not a divisor of 9157)
9157 / 9157 = 1 (the remainder is 0, so 9157 is a divisor of 9157)

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 9157 (i.e. 95.692214939356). 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 $\frac{N}{d} = D$ )

9157 / 1 = 9157 (the remainder is 0, so 1 and 9157 are divisors of 9157)
9157 / 2 = 4578.5 (the remainder is 1, so 2 is not a divisor of 9157)
9157 / 3 = 3052.3333333333 (the remainder is 1, so 3 is not a divisor of 9157)
...
9157 / 94 = 97.414893617021 (the remainder is 39, so 94 is not a divisor of 9157)
9157 / 95 = 96.389473684211 (the remainder is 37, so 95 is not a divisor of 9157)