What are the divisors of 5601?

1, 3, 1867, 5601

There is a total of 4 positive divisors.
The sum of these divisors is 7472.
The arithmetic mean is 1868.

4 odd divisors

1, 3, 1867, 5601

How to compute the divisors of 5601?

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 5601 by each of the numbers from 1 to 5601 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)

5601 / 1 = 5601 (the remainder is 0, so 1 is a divisor of 5601)
5601 / 2 = 2800.5 (the remainder is 1, so 2 is not a divisor of 5601)
5601 / 3 = 1867 (the remainder is 0, so 3 is a divisor of 5601)
...
5601 / 5600 = 1.0001785714286 (the remainder is 1, so 5600 is not a divisor of 5601)
5601 / 5601 = 1 (the remainder is 0, so 5601 is a divisor of 5601)

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 5601 (i.e. 74.839828968271). 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 $\frac{N}{d} = D$ )

5601 / 1 = 5601 (the remainder is 0, so 1 and 5601 are divisors of 5601)
5601 / 2 = 2800.5 (the remainder is 1, so 2 is not a divisor of 5601)
5601 / 3 = 1867 (the remainder is 0, so 3 and 1867 are divisors of 5601)
...
5601 / 73 = 76.72602739726 (the remainder is 53, so 73 is not a divisor of 5601)
5601 / 74 = 75.689189189189 (the remainder is 51, so 74 is not a divisor of 5601)