What are the divisors of 9149?

1, 7, 1307, 9149

There is a total of 4 positive divisors.
The sum of these divisors is 10464.
The arithmetic mean is 2616.

4 odd divisors

1, 7, 1307, 9149

How to compute the divisors of 9149?

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 9149 by each of the numbers from 1 to 9149 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)

9149 / 1 = 9149 (the remainder is 0, so 1 is a divisor of 9149)
9149 / 2 = 4574.5 (the remainder is 1, so 2 is not a divisor of 9149)
9149 / 3 = 3049.6666666667 (the remainder is 2, so 3 is not a divisor of 9149)
...
9149 / 9148 = 1.0001093135112 (the remainder is 1, so 9148 is not a divisor of 9149)
9149 / 9149 = 1 (the remainder is 0, so 9149 is a divisor of 9149)

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 9149 (i.e. 95.650405121986). 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 $\frac{N}{d} = D$ )

9149 / 1 = 9149 (the remainder is 0, so 1 and 9149 are divisors of 9149)
9149 / 2 = 4574.5 (the remainder is 1, so 2 is not a divisor of 9149)
9149 / 3 = 3049.6666666667 (the remainder is 2, so 3 is not a divisor of 9149)
...
9149 / 94 = 97.329787234043 (the remainder is 31, so 94 is not a divisor of 9149)
9149 / 95 = 96.305263157895 (the remainder is 29, so 95 is not a divisor of 9149)