What are the divisors of 1928?

1, 2, 4, 8, 241, 482, 964, 1928

There is a total of 8 positive divisors.
The sum of these divisors is 3630.
The arithmetic mean is 453.75.

6 even divisors

2, 4, 8, 482, 964, 1928

2 odd divisors

1, 241

How to compute the divisors of 1928?

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 1928 by each of the numbers from 1 to 1928 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)

1928 / 1 = 1928 (the remainder is 0, so 1 is a divisor of 1928)
1928 / 2 = 964 (the remainder is 0, so 2 is a divisor of 1928)
1928 / 3 = 642.66666666667 (the remainder is 2, so 3 is not a divisor of 1928)
...
1928 / 1927 = 1.0005189413596 (the remainder is 1, so 1927 is not a divisor of 1928)
1928 / 1928 = 1 (the remainder is 0, so 1928 is a divisor of 1928)

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 1928 (i.e. 43.9089968002). 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 $\frac{N}{d} = D$ )

1928 / 1 = 1928 (the remainder is 0, so 1 and 1928 are divisors of 1928)
1928 / 2 = 964 (the remainder is 0, so 2 and 964 are divisors of 1928)
1928 / 3 = 642.66666666667 (the remainder is 2, so 3 is not a divisor of 1928)
...
1928 / 42 = 45.904761904762 (the remainder is 38, so 42 is not a divisor of 1928)
1928 / 43 = 44.837209302326 (the remainder is 36, so 43 is not a divisor of 1928)