What are the divisors of 4501?

1, 7, 643, 4501

There is a total of 4 positive divisors.
The sum of these divisors is 5152.
The arithmetic mean is 1288.

4 odd divisors

1, 7, 643, 4501

How to compute the divisors of 4501?

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 4501 by each of the numbers from 1 to 4501 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)

4501 / 1 = 4501 (the remainder is 0, so 1 is a divisor of 4501)
4501 / 2 = 2250.5 (the remainder is 1, so 2 is not a divisor of 4501)
4501 / 3 = 1500.3333333333 (the remainder is 1, so 3 is not a divisor of 4501)
...
4501 / 4500 = 1.0002222222222 (the remainder is 1, so 4500 is not a divisor of 4501)
4501 / 4501 = 1 (the remainder is 0, so 4501 is a divisor of 4501)

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 4501 (i.e. 67.089492470878). 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 $\frac{N}{d} = D$ )

4501 / 1 = 4501 (the remainder is 0, so 1 and 4501 are divisors of 4501)
4501 / 2 = 2250.5 (the remainder is 1, so 2 is not a divisor of 4501)
4501 / 3 = 1500.3333333333 (the remainder is 1, so 3 is not a divisor of 4501)
...
4501 / 66 = 68.19696969697 (the remainder is 13, so 66 is not a divisor of 4501)
4501 / 67 = 67.179104477612 (the remainder is 12, so 67 is not a divisor of 4501)