What are the divisors of 3669?

1, 3, 1223, 3669

There is a total of 4 positive divisors.
The sum of these divisors is 4896.
The arithmetic mean is 1224.

4 odd divisors

1, 3, 1223, 3669

How to compute the divisors of 3669?

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 3669 by each of the numbers from 1 to 3669 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)

3669 / 1 = 3669 (the remainder is 0, so 1 is a divisor of 3669)
3669 / 2 = 1834.5 (the remainder is 1, so 2 is not a divisor of 3669)
3669 / 3 = 1223 (the remainder is 0, so 3 is a divisor of 3669)
...
3669 / 3668 = 1.0002726281352 (the remainder is 1, so 3668 is not a divisor of 3669)
3669 / 3669 = 1 (the remainder is 0, so 3669 is a divisor of 3669)

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 3669 (i.e. 60.572270883631). 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 $\frac{N}{d} = D$ )

3669 / 1 = 3669 (the remainder is 0, so 1 and 3669 are divisors of 3669)
3669 / 2 = 1834.5 (the remainder is 1, so 2 is not a divisor of 3669)
3669 / 3 = 1223 (the remainder is 0, so 3 and 1223 are divisors of 3669)
...
3669 / 59 = 62.186440677966 (the remainder is 11, so 59 is not a divisor of 3669)
3669 / 60 = 61.15 (the remainder is 9, so 60 is not a divisor of 3669)