What are the divisors of 9242?

1, 2, 4621, 9242

There is a total of 4 positive divisors.
The sum of these divisors is 13866.
The arithmetic mean is 3466.5.

2 even divisors

2, 9242

2 odd divisors

1, 4621

How to compute the divisors of 9242?

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 9242 by each of the numbers from 1 to 9242 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)

9242 / 1 = 9242 (the remainder is 0, so 1 is a divisor of 9242)
9242 / 2 = 4621 (the remainder is 0, so 2 is a divisor of 9242)
9242 / 3 = 3080.6666666667 (the remainder is 2, so 3 is not a divisor of 9242)
...
9242 / 9241 = 1.0001082133968 (the remainder is 1, so 9241 is not a divisor of 9242)
9242 / 9242 = 1 (the remainder is 0, so 9242 is a divisor of 9242)

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 9242 (i.e. 96.135321292437). 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 $\frac{N}{d} = D$ )

9242 / 1 = 9242 (the remainder is 0, so 1 and 9242 are divisors of 9242)
9242 / 2 = 4621 (the remainder is 0, so 2 and 4621 are divisors of 9242)
9242 / 3 = 3080.6666666667 (the remainder is 2, so 3 is not a divisor of 9242)
...
9242 / 95 = 97.284210526316 (the remainder is 27, so 95 is not a divisor of 9242)
9242 / 96 = 96.270833333333 (the remainder is 26, so 96 is not a divisor of 9242)