What are the divisors of 1628?

1, 2, 4, 11, 22, 37, 44, 74, 148, 407, 814, 1628

There is a total of 12 positive divisors.
The sum of these divisors is 3192.
The arithmetic mean is 266.

8 even divisors

2, 4, 22, 44, 74, 148, 814, 1628

4 odd divisors

1, 11, 37, 407

How to compute the divisors of 1628?

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 1628 by each of the numbers from 1 to 1628 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)

1628 / 1 = 1628 (the remainder is 0, so 1 is a divisor of 1628)
1628 / 2 = 814 (the remainder is 0, so 2 is a divisor of 1628)
1628 / 3 = 542.66666666667 (the remainder is 2, so 3 is not a divisor of 1628)
...
1628 / 1627 = 1.00061462815 (the remainder is 1, so 1627 is not a divisor of 1628)
1628 / 1628 = 1 (the remainder is 0, so 1628 is a divisor of 1628)

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 1628 (i.e. 40.348482003664). 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 $\frac{N}{d} = D$ )

1628 / 1 = 1628 (the remainder is 0, so 1 and 1628 are divisors of 1628)
1628 / 2 = 814 (the remainder is 0, so 2 and 814 are divisors of 1628)
1628 / 3 = 542.66666666667 (the remainder is 2, so 3 is not a divisor of 1628)
...
1628 / 39 = 41.74358974359 (the remainder is 29, so 39 is not a divisor of 1628)
1628 / 40 = 40.7 (the remainder is 28, so 40 is not a divisor of 1628)