What are the divisors of 4511?

1, 13, 347, 4511

There is a total of 4 positive divisors.
The sum of these divisors is 4872.
The arithmetic mean is 1218.

4 odd divisors

1, 13, 347, 4511

How to compute the divisors of 4511?

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 4511 by each of the numbers from 1 to 4511 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)

4511 / 1 = 4511 (the remainder is 0, so 1 is a divisor of 4511)
4511 / 2 = 2255.5 (the remainder is 1, so 2 is not a divisor of 4511)
4511 / 3 = 1503.6666666667 (the remainder is 2, so 3 is not a divisor of 4511)
...
4511 / 4510 = 1.00022172949 (the remainder is 1, so 4510 is not a divisor of 4511)
4511 / 4511 = 1 (the remainder is 0, so 4511 is a divisor of 4511)

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 4511 (i.e. 67.163978440828). 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 $\frac{N}{d} = D$ )

4511 / 1 = 4511 (the remainder is 0, so 1 and 4511 are divisors of 4511)
4511 / 2 = 2255.5 (the remainder is 1, so 2 is not a divisor of 4511)
4511 / 3 = 1503.6666666667 (the remainder is 2, so 3 is not a divisor of 4511)
...
4511 / 66 = 68.348484848485 (the remainder is 23, so 66 is not a divisor of 4511)
4511 / 67 = 67.328358208955 (the remainder is 22, so 67 is not a divisor of 4511)