What are the divisors of 3548?

1, 2, 4, 887, 1774, 3548

There is a total of 6 positive divisors.
The sum of these divisors is 6216.
The arithmetic mean is 1036.

4 even divisors

2, 4, 1774, 3548

2 odd divisors

1, 887

How to compute the divisors of 3548?

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 3548 by each of the numbers from 1 to 3548 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)

3548 / 1 = 3548 (the remainder is 0, so 1 is a divisor of 3548)
3548 / 2 = 1774 (the remainder is 0, so 2 is a divisor of 3548)
3548 / 3 = 1182.6666666667 (the remainder is 2, so 3 is not a divisor of 3548)
...
3548 / 3547 = 1.0002819283902 (the remainder is 1, so 3547 is not a divisor of 3548)
3548 / 3548 = 1 (the remainder is 0, so 3548 is a divisor of 3548)

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 3548 (i.e. 59.565090447342). 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 $\frac{N}{d} = D$ )

3548 / 1 = 3548 (the remainder is 0, so 1 and 3548 are divisors of 3548)
3548 / 2 = 1774 (the remainder is 0, so 2 and 1774 are divisors of 3548)
3548 / 3 = 1182.6666666667 (the remainder is 2, so 3 is not a divisor of 3548)
...
3548 / 58 = 61.172413793103 (the remainder is 10, so 58 is not a divisor of 3548)
3548 / 59 = 60.135593220339 (the remainder is 8, so 59 is not a divisor of 3548)