What are the divisors of 3628?

1, 2, 4, 907, 1814, 3628

There is a total of 6 positive divisors.
The sum of these divisors is 6356.
The arithmetic mean is 1059.3333333333.

4 even divisors

2, 4, 1814, 3628

2 odd divisors

1, 907

How to compute the divisors of 3628?

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 3628 by each of the numbers from 1 to 3628 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)

3628 / 1 = 3628 (the remainder is 0, so 1 is a divisor of 3628)
3628 / 2 = 1814 (the remainder is 0, so 2 is a divisor of 3628)
3628 / 3 = 1209.3333333333 (the remainder is 1, so 3 is not a divisor of 3628)
...
3628 / 3627 = 1.0002757099531 (the remainder is 1, so 3627 is not a divisor of 3628)
3628 / 3628 = 1 (the remainder is 0, so 3628 is a divisor of 3628)

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 3628 (i.e. 60.232881385502). 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 $\frac{N}{d} = D$ )

3628 / 1 = 3628 (the remainder is 0, so 1 and 3628 are divisors of 3628)
3628 / 2 = 1814 (the remainder is 0, so 2 and 1814 are divisors of 3628)
3628 / 3 = 1209.3333333333 (the remainder is 1, so 3 is not a divisor of 3628)
...
3628 / 59 = 61.491525423729 (the remainder is 29, so 59 is not a divisor of 3628)
3628 / 60 = 60.466666666667 (the remainder is 28, so 60 is not a divisor of 3628)