What are the divisors of 1642?

1, 2, 821, 1642

There is a total of 4 positive divisors.
The sum of these divisors is 2466.
The arithmetic mean is 616.5.

2 even divisors

2, 1642

2 odd divisors

1, 821

How to compute the divisors of 1642?

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 1642 by each of the numbers from 1 to 1642 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)

1642 / 1 = 1642 (the remainder is 0, so 1 is a divisor of 1642)
1642 / 2 = 821 (the remainder is 0, so 2 is a divisor of 1642)
1642 / 3 = 547.33333333333 (the remainder is 1, so 3 is not a divisor of 1642)
...
1642 / 1641 = 1.0006093845216 (the remainder is 1, so 1641 is not a divisor of 1642)
1642 / 1642 = 1 (the remainder is 0, so 1642 is a divisor of 1642)

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 1642 (i.e. 40.52159917871). 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 $\frac{N}{d} = D$ )

1642 / 1 = 1642 (the remainder is 0, so 1 and 1642 are divisors of 1642)
1642 / 2 = 821 (the remainder is 0, so 2 and 821 are divisors of 1642)
1642 / 3 = 547.33333333333 (the remainder is 1, so 3 is not a divisor of 1642)
...
1642 / 39 = 42.102564102564 (the remainder is 4, so 39 is not a divisor of 1642)
1642 / 40 = 41.05 (the remainder is 2, so 40 is not a divisor of 1642)