What are the divisors of 9244?

1, 2, 4, 2311, 4622, 9244

There is a total of 6 positive divisors.
The sum of these divisors is 16184.
The arithmetic mean is 2697.3333333333.

4 even divisors

2, 4, 4622, 9244

2 odd divisors

1, 2311

How to compute the divisors of 9244?

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 9244 by each of the numbers from 1 to 9244 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)

9244 / 1 = 9244 (the remainder is 0, so 1 is a divisor of 9244)
9244 / 2 = 4622 (the remainder is 0, so 2 is a divisor of 9244)
9244 / 3 = 3081.3333333333 (the remainder is 1, so 3 is not a divisor of 9244)
...
9244 / 9243 = 1.0001081899816 (the remainder is 1, so 9243 is not a divisor of 9244)
9244 / 9244 = 1 (the remainder is 0, so 9244 is a divisor of 9244)

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 9244 (i.e. 96.145722733775). 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 $\frac{N}{d} = D$ )

9244 / 1 = 9244 (the remainder is 0, so 1 and 9244 are divisors of 9244)
9244 / 2 = 4622 (the remainder is 0, so 2 and 4622 are divisors of 9244)
9244 / 3 = 3081.3333333333 (the remainder is 1, so 3 is not a divisor of 9244)
...
9244 / 95 = 97.305263157895 (the remainder is 29, so 95 is not a divisor of 9244)
9244 / 96 = 96.291666666667 (the remainder is 28, so 96 is not a divisor of 9244)