What are the divisors of 9172?

1, 2, 4, 2293, 4586, 9172

There is a total of 6 positive divisors.
The sum of these divisors is 16058.
The arithmetic mean is 2676.3333333333.

4 even divisors

2, 4, 4586, 9172

2 odd divisors

1, 2293

How to compute the divisors of 9172?

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 9172 by each of the numbers from 1 to 9172 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)

9172 / 1 = 9172 (the remainder is 0, so 1 is a divisor of 9172)
9172 / 2 = 4586 (the remainder is 0, so 2 is a divisor of 9172)
9172 / 3 = 3057.3333333333 (the remainder is 1, so 3 is not a divisor of 9172)
...
9172 / 9171 = 1.0001090393632 (the remainder is 1, so 9171 is not a divisor of 9172)
9172 / 9172 = 1 (the remainder is 0, so 9172 is a divisor of 9172)

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 9172 (i.e. 95.770559150503). 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 $\frac{N}{d} = D$ )

9172 / 1 = 9172 (the remainder is 0, so 1 and 9172 are divisors of 9172)
9172 / 2 = 4586 (the remainder is 0, so 2 and 4586 are divisors of 9172)
9172 / 3 = 3057.3333333333 (the remainder is 1, so 3 is not a divisor of 9172)
...
9172 / 94 = 97.574468085106 (the remainder is 54, so 94 is not a divisor of 9172)
9172 / 95 = 96.547368421053 (the remainder is 52, so 95 is not a divisor of 9172)