What are the divisors of 608?

1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608

There is a total of 12 positive divisors.
The sum of these divisors is 1260.
The arithmetic mean is 105.

10 even divisors

2, 4, 8, 16, 32, 38, 76, 152, 304, 608

2 odd divisors

1, 19

How to compute the divisors of 608?

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 608 by each of the numbers from 1 to 608 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)

608 / 1 = 608 (the remainder is 0, so 1 is a divisor of 608)
608 / 2 = 304 (the remainder is 0, so 2 is a divisor of 608)
608 / 3 = 202.66666666667 (the remainder is 2, so 3 is not a divisor of 608)
...
608 / 607 = 1.001647446458 (the remainder is 1, so 607 is not a divisor of 608)
608 / 608 = 1 (the remainder is 0, so 608 is a divisor of 608)

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 608 (i.e. 24.657656011876). 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 $\frac{N}{d} = D$ )

608 / 1 = 608 (the remainder is 0, so 1 and 608 are divisors of 608)
608 / 2 = 304 (the remainder is 0, so 2 and 304 are divisors of 608)
608 / 3 = 202.66666666667 (the remainder is 2, so 3 is not a divisor of 608)
...
608 / 23 = 26.434782608696 (the remainder is 10, so 23 is not a divisor of 608)
608 / 24 = 25.333333333333 (the remainder is 8, so 24 is not a divisor of 608)