What are the divisors of 9642?

1, 2, 3, 6, 1607, 3214, 4821, 9642

There is a total of 8 positive divisors.
The sum of these divisors is 19296.
The arithmetic mean is 2412.

4 even divisors

2, 6, 3214, 9642

4 odd divisors

1, 3, 1607, 4821

How to compute the divisors of 9642?

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 9642 by each of the numbers from 1 to 9642 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)

9642 / 1 = 9642 (the remainder is 0, so 1 is a divisor of 9642)
9642 / 2 = 4821 (the remainder is 0, so 2 is a divisor of 9642)
9642 / 3 = 3214 (the remainder is 0, so 3 is a divisor of 9642)
...
9642 / 9641 = 1.0001037236801 (the remainder is 1, so 9641 is not a divisor of 9642)
9642 / 9642 = 1 (the remainder is 0, so 9642 is a divisor of 9642)

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 9642 (i.e. 98.193686151402). 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 $\frac{N}{d} = D$ )

9642 / 1 = 9642 (the remainder is 0, so 1 and 9642 are divisors of 9642)
9642 / 2 = 4821 (the remainder is 0, so 2 and 4821 are divisors of 9642)
9642 / 3 = 3214 (the remainder is 0, so 3 and 3214 are divisors of 9642)
...
9642 / 97 = 99.40206185567 (the remainder is 39, so 97 is not a divisor of 9642)
9642 / 98 = 98.387755102041 (the remainder is 38, so 98 is not a divisor of 9642)