What are the divisors of 9179?

1, 67, 137, 9179

There is a total of 4 positive divisors.
The sum of these divisors is 9384.
The arithmetic mean is 2346.

4 odd divisors

1, 67, 137, 9179

How to compute the divisors of 9179?

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 9179 by each of the numbers from 1 to 9179 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)

9179 / 1 = 9179 (the remainder is 0, so 1 is a divisor of 9179)
9179 / 2 = 4589.5 (the remainder is 1, so 2 is not a divisor of 9179)
9179 / 3 = 3059.6666666667 (the remainder is 2, so 3 is not a divisor of 9179)
...
9179 / 9178 = 1.0001089561996 (the remainder is 1, so 9178 is not a divisor of 9179)
9179 / 9179 = 1 (the remainder is 0, so 9179 is a divisor of 9179)

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 9179 (i.e. 95.807097858144). 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 $\frac{N}{d} = D$ )

9179 / 1 = 9179 (the remainder is 0, so 1 and 9179 are divisors of 9179)
9179 / 2 = 4589.5 (the remainder is 1, so 2 is not a divisor of 9179)
9179 / 3 = 3059.6666666667 (the remainder is 2, so 3 is not a divisor of 9179)
...
9179 / 94 = 97.648936170213 (the remainder is 61, so 94 is not a divisor of 9179)
9179 / 95 = 96.621052631579 (the remainder is 59, so 95 is not a divisor of 9179)