What are the divisors of 3667?

1, 19, 193, 3667

There is a total of 4 positive divisors.
The sum of these divisors is 3880.
The arithmetic mean is 970.

4 odd divisors

1, 19, 193, 3667

How to compute the divisors of 3667?

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 3667 by each of the numbers from 1 to 3667 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)

3667 / 1 = 3667 (the remainder is 0, so 1 is a divisor of 3667)
3667 / 2 = 1833.5 (the remainder is 1, so 2 is not a divisor of 3667)
3667 / 3 = 1222.3333333333 (the remainder is 1, so 3 is not a divisor of 3667)
...
3667 / 3666 = 1.0002727768685 (the remainder is 1, so 3666 is not a divisor of 3667)
3667 / 3667 = 1 (the remainder is 0, so 3667 is a divisor of 3667)

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 3667 (i.e. 60.555759428811). 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 $\frac{N}{d} = D$ )

3667 / 1 = 3667 (the remainder is 0, so 1 and 3667 are divisors of 3667)
3667 / 2 = 1833.5 (the remainder is 1, so 2 is not a divisor of 3667)
3667 / 3 = 1222.3333333333 (the remainder is 1, so 3 is not a divisor of 3667)
...
3667 / 59 = 62.152542372881 (the remainder is 9, so 59 is not a divisor of 3667)
3667 / 60 = 61.116666666667 (the remainder is 7, so 60 is not a divisor of 3667)