What are the divisors of 1904?

1, 2, 4, 7, 8, 14, 16, 17, 28, 34, 56, 68, 112, 119, 136, 238, 272, 476, 952, 1904

There is a total of 20 positive divisors.
The sum of these divisors is 4464.
The arithmetic mean is 223.2.

16 even divisors

2, 4, 8, 14, 16, 28, 34, 56, 68, 112, 136, 238, 272, 476, 952, 1904

4 odd divisors

1, 7, 17, 119

How to compute the divisors of 1904?

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 1904 by each of the numbers from 1 to 1904 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)

1904 / 1 = 1904 (the remainder is 0, so 1 is a divisor of 1904)
1904 / 2 = 952 (the remainder is 0, so 2 is a divisor of 1904)
1904 / 3 = 634.66666666667 (the remainder is 2, so 3 is not a divisor of 1904)
...
1904 / 1903 = 1.0005254860746 (the remainder is 1, so 1903 is not a divisor of 1904)
1904 / 1904 = 1 (the remainder is 0, so 1904 is a divisor of 1904)

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 1904 (i.e. 43.634848458543). 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 $\frac{N}{d} = D$ )

1904 / 1 = 1904 (the remainder is 0, so 1 and 1904 are divisors of 1904)
1904 / 2 = 952 (the remainder is 0, so 2 and 952 are divisors of 1904)
1904 / 3 = 634.66666666667 (the remainder is 2, so 3 is not a divisor of 1904)
...
1904 / 42 = 45.333333333333 (the remainder is 14, so 42 is not a divisor of 1904)
1904 / 43 = 44.279069767442 (the remainder is 12, so 43 is not a divisor of 1904)