What are the divisors of 9604?

1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604

There is a total of 15 positive divisors.
The sum of these divisors is 19607.
The arithmetic mean is 1307.1333333333.

10 even divisors

2, 4, 14, 28, 98, 196, 686, 1372, 4802, 9604

5 odd divisors

1, 7, 49, 343, 2401

How to compute the divisors of 9604?

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 9604 by each of the numbers from 1 to 9604 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)

9604 / 1 = 9604 (the remainder is 0, so 1 is a divisor of 9604)
9604 / 2 = 4802 (the remainder is 0, so 2 is a divisor of 9604)
9604 / 3 = 3201.3333333333 (the remainder is 1, so 3 is not a divisor of 9604)
...
9604 / 9603 = 1.0001041341248 (the remainder is 1, so 9603 is not a divisor of 9604)
9604 / 9604 = 1 (the remainder is 0, so 9604 is a divisor of 9604)

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 9604 (i.e. 98). 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 $\frac{N}{d} = D$ )

9604 / 1 = 9604 (the remainder is 0, so 1 and 9604 are divisors of 9604)
9604 / 2 = 4802 (the remainder is 0, so 2 and 4802 are divisors of 9604)
9604 / 3 = 3201.3333333333 (the remainder is 1, so 3 is not a divisor of 9604)
...
9604 / 97 = 99.010309278351 (the remainder is 1, so 97 is not a divisor of 9604)
9604 / 98 = 98 (the remainder is 0, so 98 and 98 are divisors of 9604)