What are the divisors of 9640?

1, 2, 4, 5, 8, 10, 20, 40, 241, 482, 964, 1205, 1928, 2410, 4820, 9640

There is a total of 16 positive divisors.
The sum of these divisors is 21780.
The arithmetic mean is 1361.25.

12 even divisors

2, 4, 8, 10, 20, 40, 482, 964, 1928, 2410, 4820, 9640

4 odd divisors

1, 5, 241, 1205

How to compute the divisors of 9640?

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 9640 by each of the numbers from 1 to 9640 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)

9640 / 1 = 9640 (the remainder is 0, so 1 is a divisor of 9640)
9640 / 2 = 4820 (the remainder is 0, so 2 is a divisor of 9640)
9640 / 3 = 3213.3333333333 (the remainder is 1, so 3 is not a divisor of 9640)
...
9640 / 9639 = 1.0001037452018 (the remainder is 1, so 9639 is not a divisor of 9640)
9640 / 9640 = 1 (the remainder is 0, so 9640 is a divisor of 9640)

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 9640 (i.e. 98.183501669069). 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 $\frac{N}{d} = D$ )

9640 / 1 = 9640 (the remainder is 0, so 1 and 9640 are divisors of 9640)
9640 / 2 = 4820 (the remainder is 0, so 2 and 4820 are divisors of 9640)
9640 / 3 = 3213.3333333333 (the remainder is 1, so 3 is not a divisor of 9640)
...
9640 / 97 = 99.381443298969 (the remainder is 37, so 97 is not a divisor of 9640)
9640 / 98 = 98.367346938776 (the remainder is 36, so 98 is not a divisor of 9640)