What are the divisors of 3621?

1, 3, 17, 51, 71, 213, 1207, 3621

There is a total of 8 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 648.

8 odd divisors

1, 3, 17, 51, 71, 213, 1207, 3621

How to compute the divisors of 3621?

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 3621 by each of the numbers from 1 to 3621 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)

3621 / 1 = 3621 (the remainder is 0, so 1 is a divisor of 3621)
3621 / 2 = 1810.5 (the remainder is 1, so 2 is not a divisor of 3621)
3621 / 3 = 1207 (the remainder is 0, so 3 is a divisor of 3621)
...
3621 / 3620 = 1.0002762430939 (the remainder is 1, so 3620 is not a divisor of 3621)
3621 / 3621 = 1 (the remainder is 0, so 3621 is a divisor of 3621)

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 3621 (i.e. 60.174745533322). 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 $\frac{N}{d} = D$ )

3621 / 1 = 3621 (the remainder is 0, so 1 and 3621 are divisors of 3621)
3621 / 2 = 1810.5 (the remainder is 1, so 2 is not a divisor of 3621)
3621 / 3 = 1207 (the remainder is 0, so 3 and 1207 are divisors of 3621)
...
3621 / 59 = 61.372881355932 (the remainder is 22, so 59 is not a divisor of 3621)
3621 / 60 = 60.35 (the remainder is 21, so 60 is not a divisor of 3621)