What are the divisors of 4611?

1, 3, 29, 53, 87, 159, 1537, 4611

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

8 odd divisors

1, 3, 29, 53, 87, 159, 1537, 4611

How to compute the divisors of 4611?

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 4611 by each of the numbers from 1 to 4611 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)

4611 / 1 = 4611 (the remainder is 0, so 1 is a divisor of 4611)
4611 / 2 = 2305.5 (the remainder is 1, so 2 is not a divisor of 4611)
4611 / 3 = 1537 (the remainder is 0, so 3 is a divisor of 4611)
...
4611 / 4610 = 1.0002169197397 (the remainder is 1, so 4610 is not a divisor of 4611)
4611 / 4611 = 1 (the remainder is 0, so 4611 is a divisor of 4611)

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 4611 (i.e. 67.90434448546). 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 $\frac{N}{d} = D$ )

4611 / 1 = 4611 (the remainder is 0, so 1 and 4611 are divisors of 4611)
4611 / 2 = 2305.5 (the remainder is 1, so 2 is not a divisor of 4611)
4611 / 3 = 1537 (the remainder is 0, so 3 and 1537 are divisors of 4611)
...
4611 / 66 = 69.863636363636 (the remainder is 57, so 66 is not a divisor of 4611)
4611 / 67 = 68.820895522388 (the remainder is 55, so 67 is not a divisor of 4611)