What are the divisors of 3611?

1, 23, 157, 3611

There is a total of 4 positive divisors.
The sum of these divisors is 3792.
The arithmetic mean is 948.

4 odd divisors

1, 23, 157, 3611

How to compute the divisors of 3611?

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 3611 by each of the numbers from 1 to 3611 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)

3611 / 1 = 3611 (the remainder is 0, so 1 is a divisor of 3611)
3611 / 2 = 1805.5 (the remainder is 1, so 2 is not a divisor of 3611)
3611 / 3 = 1203.6666666667 (the remainder is 2, so 3 is not a divisor of 3611)
...
3611 / 3610 = 1.0002770083102 (the remainder is 1, so 3610 is not a divisor of 3611)
3611 / 3611 = 1 (the remainder is 0, so 3611 is a divisor of 3611)

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 3611 (i.e. 60.091596750294). 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 $\frac{N}{d} = D$ )

3611 / 1 = 3611 (the remainder is 0, so 1 and 3611 are divisors of 3611)
3611 / 2 = 1805.5 (the remainder is 1, so 2 is not a divisor of 3611)
3611 / 3 = 1203.6666666667 (the remainder is 2, so 3 is not a divisor of 3611)
...
3611 / 59 = 61.203389830508 (the remainder is 12, so 59 is not a divisor of 3611)
3611 / 60 = 60.183333333333 (the remainder is 11, so 60 is not a divisor of 3611)