What are the divisors of 4557?

1, 3, 7, 21, 31, 49, 93, 147, 217, 651, 1519, 4557

There is a total of 12 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 608.

12 odd divisors

1, 3, 7, 21, 31, 49, 93, 147, 217, 651, 1519, 4557

How to compute the divisors of 4557?

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 4557 by each of the numbers from 1 to 4557 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)

4557 / 1 = 4557 (the remainder is 0, so 1 is a divisor of 4557)
4557 / 2 = 2278.5 (the remainder is 1, so 2 is not a divisor of 4557)
4557 / 3 = 1519 (the remainder is 0, so 3 is a divisor of 4557)
...
4557 / 4556 = 1.0002194907814 (the remainder is 1, so 4556 is not a divisor of 4557)
4557 / 4557 = 1 (the remainder is 0, so 4557 is a divisor of 4557)

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 4557 (i.e. 67.505555326951). 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 $\frac{N}{d} = D$ )

4557 / 1 = 4557 (the remainder is 0, so 1 and 4557 are divisors of 4557)
4557 / 2 = 2278.5 (the remainder is 1, so 2 is not a divisor of 4557)
4557 / 3 = 1519 (the remainder is 0, so 3 and 1519 are divisors of 4557)
...
4557 / 66 = 69.045454545455 (the remainder is 3, so 66 is not a divisor of 4557)
4557 / 67 = 68.014925373134 (the remainder is 1, so 67 is not a divisor of 4557)