What are the divisors of 3488?

1, 2, 4, 8, 16, 32, 109, 218, 436, 872, 1744, 3488

There is a total of 12 positive divisors.
The sum of these divisors is 6930.
The arithmetic mean is 577.5.

10 even divisors

2, 4, 8, 16, 32, 218, 436, 872, 1744, 3488

2 odd divisors

1, 109

How to compute the divisors of 3488?

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 3488 by each of the numbers from 1 to 3488 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)

3488 / 1 = 3488 (the remainder is 0, so 1 is a divisor of 3488)
3488 / 2 = 1744 (the remainder is 0, so 2 is a divisor of 3488)
3488 / 3 = 1162.6666666667 (the remainder is 2, so 3 is not a divisor of 3488)
...
3488 / 3487 = 1.0002867794666 (the remainder is 1, so 3487 is not a divisor of 3488)
3488 / 3488 = 1 (the remainder is 0, so 3488 is a divisor of 3488)

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 3488 (i.e. 59.059292240934). 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 $\frac{N}{d} = D$ )

3488 / 1 = 3488 (the remainder is 0, so 1 and 3488 are divisors of 3488)
3488 / 2 = 1744 (the remainder is 0, so 2 and 1744 are divisors of 3488)
3488 / 3 = 1162.6666666667 (the remainder is 2, so 3 is not a divisor of 3488)
...
3488 / 58 = 60.137931034483 (the remainder is 8, so 58 is not a divisor of 3488)
3488 / 59 = 59.118644067797 (the remainder is 7, so 59 is not a divisor of 3488)