What are the divisors of 3601?

1, 13, 277, 3601

There is a total of 4 positive divisors.
The sum of these divisors is 3892.
The arithmetic mean is 973.

4 odd divisors

1, 13, 277, 3601

How to compute the divisors of 3601?

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 3601 by each of the numbers from 1 to 3601 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)

3601 / 1 = 3601 (the remainder is 0, so 1 is a divisor of 3601)
3601 / 2 = 1800.5 (the remainder is 1, so 2 is not a divisor of 3601)
3601 / 3 = 1200.3333333333 (the remainder is 1, so 3 is not a divisor of 3601)
...
3601 / 3600 = 1.0002777777778 (the remainder is 1, so 3600 is not a divisor of 3601)
3601 / 3601 = 1 (the remainder is 0, so 3601 is a divisor of 3601)

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 3601 (i.e. 60.00833275471). 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 $\frac{N}{d} = D$ )

3601 / 1 = 3601 (the remainder is 0, so 1 and 3601 are divisors of 3601)
3601 / 2 = 1800.5 (the remainder is 1, so 2 is not a divisor of 3601)
3601 / 3 = 1200.3333333333 (the remainder is 1, so 3 is not a divisor of 3601)
...
3601 / 59 = 61.033898305085 (the remainder is 2, so 59 is not a divisor of 3601)
3601 / 60 = 60.016666666667 (the remainder is 1, so 60 is not a divisor of 3601)