What are the divisors of 3671?

1, 3671

There is a total of 2 positive divisors.
The sum of these divisors is 3672.
The arithmetic mean is 1836.

2 odd divisors

1, 3671

How to compute the divisors of 3671?

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 3671 by each of the numbers from 1 to 3671 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)

3671 / 1 = 3671 (the remainder is 0, so 1 is a divisor of 3671)
3671 / 2 = 1835.5 (the remainder is 1, so 2 is not a divisor of 3671)
3671 / 3 = 1223.6666666667 (the remainder is 2, so 3 is not a divisor of 3671)
...
3671 / 3670 = 1.000272479564 (the remainder is 1, so 3670 is not a divisor of 3671)
3671 / 3671 = 1 (the remainder is 0, so 3671 is a divisor of 3671)

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 3671 (i.e. 60.588777838804). 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 $\frac{N}{d} = D$ )

3671 / 1 = 3671 (the remainder is 0, so 1 and 3671 are divisors of 3671)
3671 / 2 = 1835.5 (the remainder is 1, so 2 is not a divisor of 3671)
3671 / 3 = 1223.6666666667 (the remainder is 2, so 3 is not a divisor of 3671)
...
3671 / 59 = 62.220338983051 (the remainder is 13, so 59 is not a divisor of 3671)
3671 / 60 = 61.183333333333 (the remainder is 11, so 60 is not a divisor of 3671)