What are the divisors of 3603?

1, 3, 1201, 3603

There is a total of 4 positive divisors.
The sum of these divisors is 4808.
The arithmetic mean is 1202.

4 odd divisors

1, 3, 1201, 3603

How to compute the divisors of 3603?

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 3603 by each of the numbers from 1 to 3603 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)

3603 / 1 = 3603 (the remainder is 0, so 1 is a divisor of 3603)
3603 / 2 = 1801.5 (the remainder is 1, so 2 is not a divisor of 3603)
3603 / 3 = 1201 (the remainder is 0, so 3 is a divisor of 3603)
...
3603 / 3602 = 1.0002776235425 (the remainder is 1, so 3602 is not a divisor of 3603)
3603 / 3603 = 1 (the remainder is 0, so 3603 is a divisor of 3603)

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 3603 (i.e. 60.024994793836). 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 $\frac{N}{d} = D$ )

3603 / 1 = 3603 (the remainder is 0, so 1 and 3603 are divisors of 3603)
3603 / 2 = 1801.5 (the remainder is 1, so 2 is not a divisor of 3603)
3603 / 3 = 1201 (the remainder is 0, so 3 and 1201 are divisors of 3603)
...
3603 / 59 = 61.067796610169 (the remainder is 4, so 59 is not a divisor of 3603)
3603 / 60 = 60.05 (the remainder is 3, so 60 is not a divisor of 3603)