What are the divisors of 3545?

1, 5, 709, 3545

There is a total of 4 positive divisors.
The sum of these divisors is 4260.
The arithmetic mean is 1065.

4 odd divisors

1, 5, 709, 3545

How to compute the divisors of 3545?

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 3545 by each of the numbers from 1 to 3545 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)

3545 / 1 = 3545 (the remainder is 0, so 1 is a divisor of 3545)
3545 / 2 = 1772.5 (the remainder is 1, so 2 is not a divisor of 3545)
3545 / 3 = 1181.6666666667 (the remainder is 2, so 3 is not a divisor of 3545)
...
3545 / 3544 = 1.0002821670429 (the remainder is 1, so 3544 is not a divisor of 3545)
3545 / 3545 = 1 (the remainder is 0, so 3545 is a divisor of 3545)

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 3545 (i.e. 59.539902586417). 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 $\frac{N}{d} = D$ )

3545 / 1 = 3545 (the remainder is 0, so 1 and 3545 are divisors of 3545)
3545 / 2 = 1772.5 (the remainder is 1, so 2 is not a divisor of 3545)
3545 / 3 = 1181.6666666667 (the remainder is 2, so 3 is not a divisor of 3545)
...
3545 / 58 = 61.120689655172 (the remainder is 7, so 58 is not a divisor of 3545)
3545 / 59 = 60.084745762712 (the remainder is 5, so 59 is not a divisor of 3545)