What are the divisors of 1604?

1, 2, 4, 401, 802, 1604

There is a total of 6 positive divisors.
The sum of these divisors is 2814.
The arithmetic mean is 469.

4 even divisors

2, 4, 802, 1604

2 odd divisors

1, 401

How to compute the divisors of 1604?

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 1604 by each of the numbers from 1 to 1604 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)

1604 / 1 = 1604 (the remainder is 0, so 1 is a divisor of 1604)
1604 / 2 = 802 (the remainder is 0, so 2 is a divisor of 1604)
1604 / 3 = 534.66666666667 (the remainder is 2, so 3 is not a divisor of 1604)
...
1604 / 1603 = 1.0006238303182 (the remainder is 1, so 1603 is not a divisor of 1604)
1604 / 1604 = 1 (the remainder is 0, so 1604 is a divisor of 1604)

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 1604 (i.e. 40.049968789002). 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 $\frac{N}{d} = D$ )

1604 / 1 = 1604 (the remainder is 0, so 1 and 1604 are divisors of 1604)
1604 / 2 = 802 (the remainder is 0, so 2 and 802 are divisors of 1604)
1604 / 3 = 534.66666666667 (the remainder is 2, so 3 is not a divisor of 1604)
...
1604 / 39 = 41.128205128205 (the remainder is 5, so 39 is not a divisor of 1604)
1604 / 40 = 40.1 (the remainder is 4, so 40 is not a divisor of 1604)