What are the divisors of 9062?

1, 2, 23, 46, 197, 394, 4531, 9062

There is a total of 8 positive divisors.
The sum of these divisors is 14256.
The arithmetic mean is 1782.

4 even divisors

2, 46, 394, 9062

4 odd divisors

1, 23, 197, 4531

How to compute the divisors of 9062?

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 9062 by each of the numbers from 1 to 9062 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)

9062 / 1 = 9062 (the remainder is 0, so 1 is a divisor of 9062)
9062 / 2 = 4531 (the remainder is 0, so 2 is a divisor of 9062)
9062 / 3 = 3020.6666666667 (the remainder is 2, so 3 is not a divisor of 9062)
...
9062 / 9061 = 1.0001103630946 (the remainder is 1, so 9061 is not a divisor of 9062)
9062 / 9062 = 1 (the remainder is 0, so 9062 is a divisor of 9062)

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 9062 (i.e. 95.194537658418). 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 $\frac{N}{d} = D$ )

9062 / 1 = 9062 (the remainder is 0, so 1 and 9062 are divisors of 9062)
9062 / 2 = 4531 (the remainder is 0, so 2 and 4531 are divisors of 9062)
9062 / 3 = 3020.6666666667 (the remainder is 2, so 3 is not a divisor of 9062)
...
9062 / 94 = 96.404255319149 (the remainder is 38, so 94 is not a divisor of 9062)
9062 / 95 = 95.389473684211 (the remainder is 37, so 95 is not a divisor of 9062)