What are the divisors of 3557?

1, 3557

There is a total of 2 positive divisors.
The sum of these divisors is 3558.
The arithmetic mean is 1779.

2 odd divisors

1, 3557

How to compute the divisors of 3557?

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 3557 by each of the numbers from 1 to 3557 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)

3557 / 1 = 3557 (the remainder is 0, so 1 is a divisor of 3557)
3557 / 2 = 1778.5 (the remainder is 1, so 2 is not a divisor of 3557)
3557 / 3 = 1185.6666666667 (the remainder is 2, so 3 is not a divisor of 3557)
...
3557 / 3556 = 1.0002812148481 (the remainder is 1, so 3556 is not a divisor of 3557)
3557 / 3557 = 1 (the remainder is 0, so 3557 is a divisor of 3557)

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 3557 (i.e. 59.640590204994). 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 $\frac{N}{d} = D$ )

3557 / 1 = 3557 (the remainder is 0, so 1 and 3557 are divisors of 3557)
3557 / 2 = 1778.5 (the remainder is 1, so 2 is not a divisor of 3557)
3557 / 3 = 1185.6666666667 (the remainder is 2, so 3 is not a divisor of 3557)
...
3557 / 58 = 61.327586206897 (the remainder is 19, so 58 is not a divisor of 3557)
3557 / 59 = 60.28813559322 (the remainder is 17, so 59 is not a divisor of 3557)