What are the divisors of 4551?

1, 3, 37, 41, 111, 123, 1517, 4551

There is a total of 8 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 798.

8 odd divisors

1, 3, 37, 41, 111, 123, 1517, 4551

How to compute the divisors of 4551?

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 4551 by each of the numbers from 1 to 4551 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)

4551 / 1 = 4551 (the remainder is 0, so 1 is a divisor of 4551)
4551 / 2 = 2275.5 (the remainder is 1, so 2 is not a divisor of 4551)
4551 / 3 = 1517 (the remainder is 0, so 3 is a divisor of 4551)
...
4551 / 4550 = 1.0002197802198 (the remainder is 1, so 4550 is not a divisor of 4551)
4551 / 4551 = 1 (the remainder is 0, so 4551 is a divisor of 4551)

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 4551 (i.e. 67.461099902092). 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 $\frac{N}{d} = D$ )

4551 / 1 = 4551 (the remainder is 0, so 1 and 4551 are divisors of 4551)
4551 / 2 = 2275.5 (the remainder is 1, so 2 is not a divisor of 4551)
4551 / 3 = 1517 (the remainder is 0, so 3 and 1517 are divisors of 4551)
...
4551 / 66 = 68.954545454545 (the remainder is 63, so 66 is not a divisor of 4551)
4551 / 67 = 67.925373134328 (the remainder is 62, so 67 is not a divisor of 4551)