What are the divisors of 4617?

1, 3, 9, 19, 27, 57, 81, 171, 243, 513, 1539, 4617

There is a total of 12 positive divisors.
The sum of these divisors is 7280.
The arithmetic mean is 606.66666666667.

12 odd divisors

1, 3, 9, 19, 27, 57, 81, 171, 243, 513, 1539, 4617

How to compute the divisors of 4617?

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 4617 by each of the numbers from 1 to 4617 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)

4617 / 1 = 4617 (the remainder is 0, so 1 is a divisor of 4617)
4617 / 2 = 2308.5 (the remainder is 1, so 2 is not a divisor of 4617)
4617 / 3 = 1539 (the remainder is 0, so 3 is a divisor of 4617)
...
4617 / 4616 = 1.0002166377816 (the remainder is 1, so 4616 is not a divisor of 4617)
4617 / 4617 = 1 (the remainder is 0, so 4617 is a divisor of 4617)

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 4617 (i.e. 67.948509917437). 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 $\frac{N}{d} = D$ )

4617 / 1 = 4617 (the remainder is 0, so 1 and 4617 are divisors of 4617)
4617 / 2 = 2308.5 (the remainder is 1, so 2 is not a divisor of 4617)
4617 / 3 = 1539 (the remainder is 0, so 3 and 1539 are divisors of 4617)
...
4617 / 66 = 69.954545454545 (the remainder is 63, so 66 is not a divisor of 4617)
4617 / 67 = 68.910447761194 (the remainder is 61, so 67 is not a divisor of 4617)