What are the divisors of 3661?

1, 7, 523, 3661

There is a total of 4 positive divisors.
The sum of these divisors is 4192.
The arithmetic mean is 1048.

4 odd divisors

1, 7, 523, 3661

How to compute the divisors of 3661?

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 3661 by each of the numbers from 1 to 3661 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)

3661 / 1 = 3661 (the remainder is 0, so 1 is a divisor of 3661)
3661 / 2 = 1830.5 (the remainder is 1, so 2 is not a divisor of 3661)
3661 / 3 = 1220.3333333333 (the remainder is 1, so 3 is not a divisor of 3661)
...
3661 / 3660 = 1.0002732240437 (the remainder is 1, so 3660 is not a divisor of 3661)
3661 / 3661 = 1 (the remainder is 0, so 3661 is a divisor of 3661)

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 3661 (i.e. 60.506198029623). 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 $\frac{N}{d} = D$ )

3661 / 1 = 3661 (the remainder is 0, so 1 and 3661 are divisors of 3661)
3661 / 2 = 1830.5 (the remainder is 1, so 2 is not a divisor of 3661)
3661 / 3 = 1220.3333333333 (the remainder is 1, so 3 is not a divisor of 3661)
...
3661 / 59 = 62.050847457627 (the remainder is 3, so 59 is not a divisor of 3661)
3661 / 60 = 61.016666666667 (the remainder is 1, so 60 is not a divisor of 3661)