What are the divisors of 9139?

1, 13, 19, 37, 247, 481, 703, 9139

There is a total of 8 positive divisors.
The sum of these divisors is 10640.
The arithmetic mean is 1330.

8 odd divisors

1, 13, 19, 37, 247, 481, 703, 9139

How to compute the divisors of 9139?

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 9139 by each of the numbers from 1 to 9139 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)

9139 / 1 = 9139 (the remainder is 0, so 1 is a divisor of 9139)
9139 / 2 = 4569.5 (the remainder is 1, so 2 is not a divisor of 9139)
9139 / 3 = 3046.3333333333 (the remainder is 1, so 3 is not a divisor of 9139)
...
9139 / 9138 = 1.0001094331364 (the remainder is 1, so 9138 is not a divisor of 9139)
9139 / 9139 = 1 (the remainder is 0, so 9139 is a divisor of 9139)

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 9139 (i.e. 95.59811713627). 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 $\frac{N}{d} = D$ )

9139 / 1 = 9139 (the remainder is 0, so 1 and 9139 are divisors of 9139)
9139 / 2 = 4569.5 (the remainder is 1, so 2 is not a divisor of 9139)
9139 / 3 = 3046.3333333333 (the remainder is 1, so 3 is not a divisor of 9139)
...
9139 / 94 = 97.223404255319 (the remainder is 21, so 94 is not a divisor of 9139)
9139 / 95 = 96.2 (the remainder is 19, so 95 is not a divisor of 9139)