What are the divisors of 4497?

1, 3, 1499, 4497

There is a total of 4 positive divisors.
The sum of these divisors is 6000.
The arithmetic mean is 1500.

4 odd divisors

1, 3, 1499, 4497

How to compute the divisors of 4497?

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 4497 by each of the numbers from 1 to 4497 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)

4497 / 1 = 4497 (the remainder is 0, so 1 is a divisor of 4497)
4497 / 2 = 2248.5 (the remainder is 1, so 2 is not a divisor of 4497)
4497 / 3 = 1499 (the remainder is 0, so 3 is a divisor of 4497)
...
4497 / 4496 = 1.0002224199288 (the remainder is 1, so 4496 is not a divisor of 4497)
4497 / 4497 = 1 (the remainder is 0, so 4497 is a divisor of 4497)

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 4497 (i.e. 67.059674917196). 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 $\frac{N}{d} = D$ )

4497 / 1 = 4497 (the remainder is 0, so 1 and 4497 are divisors of 4497)
4497 / 2 = 2248.5 (the remainder is 1, so 2 is not a divisor of 4497)
4497 / 3 = 1499 (the remainder is 0, so 3 and 1499 are divisors of 4497)
...
4497 / 66 = 68.136363636364 (the remainder is 9, so 66 is not a divisor of 4497)
4497 / 67 = 67.119402985075 (the remainder is 8, so 67 is not a divisor of 4497)