What are the divisors of 1888?

1, 2, 4, 8, 16, 32, 59, 118, 236, 472, 944, 1888

There is a total of 12 positive divisors.
The sum of these divisors is 3780.
The arithmetic mean is 315.

10 even divisors

2, 4, 8, 16, 32, 118, 236, 472, 944, 1888

2 odd divisors

1, 59

How to compute the divisors of 1888?

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 1888 by each of the numbers from 1 to 1888 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)

1888 / 1 = 1888 (the remainder is 0, so 1 is a divisor of 1888)
1888 / 2 = 944 (the remainder is 0, so 2 is a divisor of 1888)
1888 / 3 = 629.33333333333 (the remainder is 1, so 3 is not a divisor of 1888)
...
1888 / 1887 = 1.0005299417064 (the remainder is 1, so 1887 is not a divisor of 1888)
1888 / 1888 = 1 (the remainder is 0, so 1888 is a divisor of 1888)

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 1888 (i.e. 43.451121964801). 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 $\frac{N}{d} = D$ )

1888 / 1 = 1888 (the remainder is 0, so 1 and 1888 are divisors of 1888)
1888 / 2 = 944 (the remainder is 0, so 2 and 944 are divisors of 1888)
1888 / 3 = 629.33333333333 (the remainder is 1, so 3 is not a divisor of 1888)
...
1888 / 42 = 44.952380952381 (the remainder is 40, so 42 is not a divisor of 1888)
1888 / 43 = 43.906976744186 (the remainder is 39, so 43 is not a divisor of 1888)