What are the divisors of 4513?

1, 4513

There is a total of 2 positive divisors.
The sum of these divisors is 4514.
The arithmetic mean is 2257.

2 odd divisors

1, 4513

How to compute the divisors of 4513?

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 4513 by each of the numbers from 1 to 4513 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)

4513 / 1 = 4513 (the remainder is 0, so 1 is a divisor of 4513)
4513 / 2 = 2256.5 (the remainder is 1, so 2 is not a divisor of 4513)
4513 / 3 = 1504.3333333333 (the remainder is 1, so 3 is not a divisor of 4513)
...
4513 / 4512 = 1.0002216312057 (the remainder is 1, so 4512 is not a divisor of 4513)
4513 / 4513 = 1 (the remainder is 0, so 4513 is a divisor of 4513)

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 4513 (i.e. 67.178865724274). 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 $\frac{N}{d} = D$ )

4513 / 1 = 4513 (the remainder is 0, so 1 and 4513 are divisors of 4513)
4513 / 2 = 2256.5 (the remainder is 1, so 2 is not a divisor of 4513)
4513 / 3 = 1504.3333333333 (the remainder is 1, so 3 is not a divisor of 4513)
...
4513 / 66 = 68.378787878788 (the remainder is 25, so 66 is not a divisor of 4513)
4513 / 67 = 67.358208955224 (the remainder is 24, so 67 is not a divisor of 4513)