What are the divisors of 1634?

1, 2, 19, 38, 43, 86, 817, 1634

There is a total of 8 positive divisors.
The sum of these divisors is 2640.
The arithmetic mean is 330.

4 even divisors

2, 38, 86, 1634

4 odd divisors

1, 19, 43, 817

How to compute the divisors of 1634?

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 1634 by each of the numbers from 1 to 1634 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)

1634 / 1 = 1634 (the remainder is 0, so 1 is a divisor of 1634)
1634 / 2 = 817 (the remainder is 0, so 2 is a divisor of 1634)
1634 / 3 = 544.66666666667 (the remainder is 2, so 3 is not a divisor of 1634)
...
1634 / 1633 = 1.0006123698714 (the remainder is 1, so 1633 is not a divisor of 1634)
1634 / 1634 = 1 (the remainder is 0, so 1634 is a divisor of 1634)

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 1634 (i.e. 40.422765862815). 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 $\frac{N}{d} = D$ )

1634 / 1 = 1634 (the remainder is 0, so 1 and 1634 are divisors of 1634)
1634 / 2 = 817 (the remainder is 0, so 2 and 817 are divisors of 1634)
1634 / 3 = 544.66666666667 (the remainder is 2, so 3 is not a divisor of 1634)
...
1634 / 39 = 41.897435897436 (the remainder is 35, so 39 is not a divisor of 1634)
1634 / 40 = 40.85 (the remainder is 34, so 40 is not a divisor of 1634)