What are the divisors of 9142?

1, 2, 7, 14, 653, 1306, 4571, 9142

There is a total of 8 positive divisors.
The sum of these divisors is 15696.
The arithmetic mean is 1962.

4 even divisors

2, 14, 1306, 9142

4 odd divisors

1, 7, 653, 4571

How to compute the divisors of 9142?

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 9142 by each of the numbers from 1 to 9142 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)

9142 / 1 = 9142 (the remainder is 0, so 1 is a divisor of 9142)
9142 / 2 = 4571 (the remainder is 0, so 2 is a divisor of 9142)
9142 / 3 = 3047.3333333333 (the remainder is 1, so 3 is not a divisor of 9142)
...
9142 / 9141 = 1.0001093972213 (the remainder is 1, so 9141 is not a divisor of 9142)
9142 / 9142 = 1 (the remainder is 0, so 9142 is a divisor of 9142)

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 9142 (i.e. 95.613806534412). 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 $\frac{N}{d} = D$ )

9142 / 1 = 9142 (the remainder is 0, so 1 and 9142 are divisors of 9142)
9142 / 2 = 4571 (the remainder is 0, so 2 and 4571 are divisors of 9142)
9142 / 3 = 3047.3333333333 (the remainder is 1, so 3 is not a divisor of 9142)
...
9142 / 94 = 97.255319148936 (the remainder is 24, so 94 is not a divisor of 9142)
9142 / 95 = 96.231578947368 (the remainder is 22, so 95 is not a divisor of 9142)