What are the divisors of 3651?

1, 3, 1217, 3651

There is a total of 4 positive divisors.
The sum of these divisors is 4872.
The arithmetic mean is 1218.

4 odd divisors

1, 3, 1217, 3651

How to compute the divisors of 3651?

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 3651 by each of the numbers from 1 to 3651 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)

3651 / 1 = 3651 (the remainder is 0, so 1 is a divisor of 3651)
3651 / 2 = 1825.5 (the remainder is 1, so 2 is not a divisor of 3651)
3651 / 3 = 1217 (the remainder is 0, so 3 is a divisor of 3651)
...
3651 / 3650 = 1.0002739726027 (the remainder is 1, so 3650 is not a divisor of 3651)
3651 / 3651 = 1 (the remainder is 0, so 3651 is a divisor of 3651)

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 3651 (i.e. 60.423505360083). 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 $\frac{N}{d} = D$ )

3651 / 1 = 3651 (the remainder is 0, so 1 and 3651 are divisors of 3651)
3651 / 2 = 1825.5 (the remainder is 1, so 2 is not a divisor of 3651)
3651 / 3 = 1217 (the remainder is 0, so 3 and 1217 are divisors of 3651)
...
3651 / 59 = 61.881355932203 (the remainder is 52, so 59 is not a divisor of 3651)
3651 / 60 = 60.85 (the remainder is 51, so 60 is not a divisor of 3651)