What are the divisors of 1616?

1, 2, 4, 8, 16, 101, 202, 404, 808, 1616

There is a total of 10 positive divisors.
The sum of these divisors is 3162.
The arithmetic mean is 316.2.

8 even divisors

2, 4, 8, 16, 202, 404, 808, 1616

2 odd divisors

1, 101

How to compute the divisors of 1616?

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 1616 by each of the numbers from 1 to 1616 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)

1616 / 1 = 1616 (the remainder is 0, so 1 is a divisor of 1616)
1616 / 2 = 808 (the remainder is 0, so 2 is a divisor of 1616)
1616 / 3 = 538.66666666667 (the remainder is 2, so 3 is not a divisor of 1616)
...
1616 / 1615 = 1.0006191950464 (the remainder is 1, so 1615 is not a divisor of 1616)
1616 / 1616 = 1 (the remainder is 0, so 1616 is a divisor of 1616)

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 1616 (i.e. 40.199502484484). 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 $\frac{N}{d} = D$ )

1616 / 1 = 1616 (the remainder is 0, so 1 and 1616 are divisors of 1616)
1616 / 2 = 808 (the remainder is 0, so 2 and 808 are divisors of 1616)
1616 / 3 = 538.66666666667 (the remainder is 2, so 3 is not a divisor of 1616)
...
1616 / 39 = 41.435897435897 (the remainder is 17, so 39 is not a divisor of 1616)
1616 / 40 = 40.4 (the remainder is 16, so 40 is not a divisor of 1616)