What are the divisors of 3547?

1, 3547

There is a total of 2 positive divisors.
The sum of these divisors is 3548.
The arithmetic mean is 1774.

2 odd divisors

1, 3547

How to compute the divisors of 3547?

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 3547 by each of the numbers from 1 to 3547 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)

3547 / 1 = 3547 (the remainder is 0, so 1 is a divisor of 3547)
3547 / 2 = 1773.5 (the remainder is 1, so 2 is not a divisor of 3547)
3547 / 3 = 1182.3333333333 (the remainder is 1, so 3 is not a divisor of 3547)
...
3547 / 3546 = 1.0002820078962 (the remainder is 1, so 3546 is not a divisor of 3547)
3547 / 3547 = 1 (the remainder is 0, so 3547 is a divisor of 3547)

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 3547 (i.e. 59.556695677312). 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 $\frac{N}{d} = D$ )

3547 / 1 = 3547 (the remainder is 0, so 1 and 3547 are divisors of 3547)
3547 / 2 = 1773.5 (the remainder is 1, so 2 is not a divisor of 3547)
3547 / 3 = 1182.3333333333 (the remainder is 1, so 3 is not a divisor of 3547)
...
3547 / 58 = 61.155172413793 (the remainder is 9, so 58 is not a divisor of 3547)
3547 / 59 = 60.118644067797 (the remainder is 7, so 59 is not a divisor of 3547)