What are the divisors of 4472?

1, 2, 4, 8, 13, 26, 43, 52, 86, 104, 172, 344, 559, 1118, 2236, 4472

There is a total of 16 positive divisors.
The sum of these divisors is 9240.
The arithmetic mean is 577.5.

12 even divisors

2, 4, 8, 26, 52, 86, 104, 172, 344, 1118, 2236, 4472

4 odd divisors

1, 13, 43, 559

How to compute the divisors of 4472?

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 4472 by each of the numbers from 1 to 4472 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)

4472 / 1 = 4472 (the remainder is 0, so 1 is a divisor of 4472)
4472 / 2 = 2236 (the remainder is 0, so 2 is a divisor of 4472)
4472 / 3 = 1490.6666666667 (the remainder is 2, so 3 is not a divisor of 4472)
...
4472 / 4471 = 1.0002236636099 (the remainder is 1, so 4471 is not a divisor of 4472)
4472 / 4472 = 1 (the remainder is 0, so 4472 is a divisor of 4472)

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 4472 (i.e. 66.873013989202). 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 $\frac{N}{d} = D$ )

4472 / 1 = 4472 (the remainder is 0, so 1 and 4472 are divisors of 4472)
4472 / 2 = 2236 (the remainder is 0, so 2 and 2236 are divisors of 4472)
4472 / 3 = 1490.6666666667 (the remainder is 2, so 3 is not a divisor of 4472)
...
4472 / 65 = 68.8 (the remainder is 52, so 65 is not a divisor of 4472)
4472 / 66 = 67.757575757576 (the remainder is 50, so 66 is not a divisor of 4472)