What are the divisors of 9610?

1, 2, 5, 10, 31, 62, 155, 310, 961, 1922, 4805, 9610

There is a total of 12 positive divisors.
The sum of these divisors is 17874.
The arithmetic mean is 1489.5.

6 even divisors

2, 10, 62, 310, 1922, 9610

6 odd divisors

1, 5, 31, 155, 961, 4805

How to compute the divisors of 9610?

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 9610 by each of the numbers from 1 to 9610 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)

9610 / 1 = 9610 (the remainder is 0, so 1 is a divisor of 9610)
9610 / 2 = 4805 (the remainder is 0, so 2 is a divisor of 9610)
9610 / 3 = 3203.3333333333 (the remainder is 1, so 3 is not a divisor of 9610)
...
9610 / 9609 = 1.0001040691019 (the remainder is 1, so 9609 is not a divisor of 9610)
9610 / 9610 = 1 (the remainder is 0, so 9610 is a divisor of 9610)

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 9610 (i.e. 98.03060746522). 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 $\frac{N}{d} = D$ )

9610 / 1 = 9610 (the remainder is 0, so 1 and 9610 are divisors of 9610)
9610 / 2 = 4805 (the remainder is 0, so 2 and 4805 are divisors of 9610)
9610 / 3 = 3203.3333333333 (the remainder is 1, so 3 is not a divisor of 9610)
...
9610 / 97 = 99.072164948454 (the remainder is 7, so 97 is not a divisor of 9610)
9610 / 98 = 98.061224489796 (the remainder is 6, so 98 is not a divisor of 9610)