What are the divisors of 3620?

1, 2, 4, 5, 10, 20, 181, 362, 724, 905, 1810, 3620

There is a total of 12 positive divisors.
The sum of these divisors is 7644.
The arithmetic mean is 637.

8 even divisors

2, 4, 10, 20, 362, 724, 1810, 3620

4 odd divisors

1, 5, 181, 905

How to compute the divisors of 3620?

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 3620 by each of the numbers from 1 to 3620 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)

3620 / 1 = 3620 (the remainder is 0, so 1 is a divisor of 3620)
3620 / 2 = 1810 (the remainder is 0, so 2 is a divisor of 3620)
3620 / 3 = 1206.6666666667 (the remainder is 2, so 3 is not a divisor of 3620)
...
3620 / 3619 = 1.0002763194253 (the remainder is 1, so 3619 is not a divisor of 3620)
3620 / 3620 = 1 (the remainder is 0, so 3620 is a divisor of 3620)

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 3620 (i.e. 60.166435825965). 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 $\frac{N}{d} = D$ )

3620 / 1 = 3620 (the remainder is 0, so 1 and 3620 are divisors of 3620)
3620 / 2 = 1810 (the remainder is 0, so 2 and 1810 are divisors of 3620)
3620 / 3 = 1206.6666666667 (the remainder is 2, so 3 is not a divisor of 3620)
...
3620 / 59 = 61.35593220339 (the remainder is 21, so 59 is not a divisor of 3620)
3620 / 60 = 60.333333333333 (the remainder is 20, so 60 is not a divisor of 3620)