What are the divisors of 3633?

1, 3, 7, 21, 173, 519, 1211, 3633

There is a total of 8 positive divisors.
The sum of these divisors is 5568.
The arithmetic mean is 696.

8 odd divisors

1, 3, 7, 21, 173, 519, 1211, 3633

How to compute the divisors of 3633?

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 3633 by each of the numbers from 1 to 3633 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)

3633 / 1 = 3633 (the remainder is 0, so 1 is a divisor of 3633)
3633 / 2 = 1816.5 (the remainder is 1, so 2 is not a divisor of 3633)
3633 / 3 = 1211 (the remainder is 0, so 3 is a divisor of 3633)
...
3633 / 3632 = 1.0002753303965 (the remainder is 1, so 3632 is not a divisor of 3633)
3633 / 3633 = 1 (the remainder is 0, so 3633 is a divisor of 3633)

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 3633 (i.e. 60.274372663679). 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 $\frac{N}{d} = D$ )

3633 / 1 = 3633 (the remainder is 0, so 1 and 3633 are divisors of 3633)
3633 / 2 = 1816.5 (the remainder is 1, so 2 is not a divisor of 3633)
3633 / 3 = 1211 (the remainder is 0, so 3 and 1211 are divisors of 3633)
...
3633 / 59 = 61.576271186441 (the remainder is 34, so 59 is not a divisor of 3633)
3633 / 60 = 60.55 (the remainder is 33, so 60 is not a divisor of 3633)