What are the divisors of 4502?

1, 2, 2251, 4502

There is a total of 4 positive divisors.
The sum of these divisors is 6756.
The arithmetic mean is 1689.

2 even divisors

2, 4502

2 odd divisors

1, 2251

How to compute the divisors of 4502?

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 4502 by each of the numbers from 1 to 4502 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)

4502 / 1 = 4502 (the remainder is 0, so 1 is a divisor of 4502)
4502 / 2 = 2251 (the remainder is 0, so 2 is a divisor of 4502)
4502 / 3 = 1500.6666666667 (the remainder is 2, so 3 is not a divisor of 4502)
...
4502 / 4501 = 1.0002221728505 (the remainder is 1, so 4501 is not a divisor of 4502)
4502 / 4502 = 1 (the remainder is 0, so 4502 is a divisor of 4502)

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 4502 (i.e. 67.096944788865). 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 $\frac{N}{d} = D$ )

4502 / 1 = 4502 (the remainder is 0, so 1 and 4502 are divisors of 4502)
4502 / 2 = 2251 (the remainder is 0, so 2 and 2251 are divisors of 4502)
4502 / 3 = 1500.6666666667 (the remainder is 2, so 3 is not a divisor of 4502)
...
4502 / 66 = 68.212121212121 (the remainder is 14, so 66 is not a divisor of 4502)
4502 / 67 = 67.194029850746 (the remainder is 13, so 67 is not a divisor of 4502)