What are the divisors of 3472?

1, 2, 4, 7, 8, 14, 16, 28, 31, 56, 62, 112, 124, 217, 248, 434, 496, 868, 1736, 3472

There is a total of 20 positive divisors.
The sum of these divisors is 7936.
The arithmetic mean is 396.8.

16 even divisors

2, 4, 8, 14, 16, 28, 56, 62, 112, 124, 248, 434, 496, 868, 1736, 3472

4 odd divisors

1, 7, 31, 217

How to compute the divisors of 3472?

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 3472 by each of the numbers from 1 to 3472 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)

3472 / 1 = 3472 (the remainder is 0, so 1 is a divisor of 3472)
3472 / 2 = 1736 (the remainder is 0, so 2 is a divisor of 3472)
3472 / 3 = 1157.3333333333 (the remainder is 1, so 3 is not a divisor of 3472)
...
3472 / 3471 = 1.0002881014117 (the remainder is 1, so 3471 is not a divisor of 3472)
3472 / 3472 = 1 (the remainder is 0, so 3472 is a divisor of 3472)

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 3472 (i.e. 58.923679450625). 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 $\frac{N}{d} = D$ )

3472 / 1 = 3472 (the remainder is 0, so 1 and 3472 are divisors of 3472)
3472 / 2 = 1736 (the remainder is 0, so 2 and 1736 are divisors of 3472)
3472 / 3 = 1157.3333333333 (the remainder is 1, so 3 is not a divisor of 3472)
...
3472 / 57 = 60.912280701754 (the remainder is 52, so 57 is not a divisor of 3472)
3472 / 58 = 59.862068965517 (the remainder is 50, so 58 is not a divisor of 3472)