What are the divisors of 3642?

1, 2, 3, 6, 607, 1214, 1821, 3642

There is a total of 8 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 912.

4 even divisors

2, 6, 1214, 3642

4 odd divisors

1, 3, 607, 1821

How to compute the divisors of 3642?

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 3642 by each of the numbers from 1 to 3642 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)

3642 / 1 = 3642 (the remainder is 0, so 1 is a divisor of 3642)
3642 / 2 = 1821 (the remainder is 0, so 2 is a divisor of 3642)
3642 / 3 = 1214 (the remainder is 0, so 3 is a divisor of 3642)
...
3642 / 3641 = 1.0002746498215 (the remainder is 1, so 3641 is not a divisor of 3642)
3642 / 3642 = 1 (the remainder is 0, so 3642 is a divisor of 3642)

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 3642 (i.e. 60.348985078458). 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 $\frac{N}{d} = D$ )

3642 / 1 = 3642 (the remainder is 0, so 1 and 3642 are divisors of 3642)
3642 / 2 = 1821 (the remainder is 0, so 2 and 1821 are divisors of 3642)
3642 / 3 = 1214 (the remainder is 0, so 3 and 1214 are divisors of 3642)
...
3642 / 59 = 61.728813559322 (the remainder is 43, so 59 is not a divisor of 3642)
3642 / 60 = 60.7 (the remainder is 42, so 60 is not a divisor of 3642)