What are the divisors of 9092?

1, 2, 4, 2273, 4546, 9092

There is a total of 6 positive divisors.
The sum of these divisors is 15918.
The arithmetic mean is 2653.

4 even divisors

2, 4, 4546, 9092

2 odd divisors

1, 2273

How to compute the divisors of 9092?

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 9092 by each of the numbers from 1 to 9092 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)

9092 / 1 = 9092 (the remainder is 0, so 1 is a divisor of 9092)
9092 / 2 = 4546 (the remainder is 0, so 2 is a divisor of 9092)
9092 / 3 = 3030.6666666667 (the remainder is 2, so 3 is not a divisor of 9092)
...
9092 / 9091 = 1.0001099989 (the remainder is 1, so 9091 is not a divisor of 9092)
9092 / 9092 = 1 (the remainder is 0, so 9092 is a divisor of 9092)

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 9092 (i.e. 95.351979528482). 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 $\frac{N}{d} = D$ )

9092 / 1 = 9092 (the remainder is 0, so 1 and 9092 are divisors of 9092)
9092 / 2 = 4546 (the remainder is 0, so 2 and 4546 are divisors of 9092)
9092 / 3 = 3030.6666666667 (the remainder is 2, so 3 is not a divisor of 9092)
...
9092 / 94 = 96.723404255319 (the remainder is 68, so 94 is not a divisor of 9092)
9092 / 95 = 95.705263157895 (the remainder is 67, so 95 is not a divisor of 9092)