What are the divisors of 4572?

1, 2, 3, 4, 6, 9, 12, 18, 36, 127, 254, 381, 508, 762, 1143, 1524, 2286, 4572

There is a total of 18 positive divisors.
The sum of these divisors is 11648.
The arithmetic mean is 647.11111111111.

12 even divisors

2, 4, 6, 12, 18, 36, 254, 508, 762, 1524, 2286, 4572

6 odd divisors

1, 3, 9, 127, 381, 1143

How to compute the divisors of 4572?

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 4572 by each of the numbers from 1 to 4572 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)

4572 / 1 = 4572 (the remainder is 0, so 1 is a divisor of 4572)
4572 / 2 = 2286 (the remainder is 0, so 2 is a divisor of 4572)
4572 / 3 = 1524 (the remainder is 0, so 3 is a divisor of 4572)
...
4572 / 4571 = 1.0002187705097 (the remainder is 1, so 4571 is not a divisor of 4572)
4572 / 4572 = 1 (the remainder is 0, so 4572 is a divisor of 4572)

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 4572 (i.e. 67.616566017508). 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 $\frac{N}{d} = D$ )

4572 / 1 = 4572 (the remainder is 0, so 1 and 4572 are divisors of 4572)
4572 / 2 = 2286 (the remainder is 0, so 2 and 2286 are divisors of 4572)
4572 / 3 = 1524 (the remainder is 0, so 3 and 1524 are divisors of 4572)
...
4572 / 66 = 69.272727272727 (the remainder is 18, so 66 is not a divisor of 4572)
4572 / 67 = 68.238805970149 (the remainder is 16, so 67 is not a divisor of 4572)