What are the divisors of 4817?

1, 4817

There is a total of 2 positive divisors.
The sum of these divisors is 4818.
The arithmetic mean is 2409.

2 odd divisors

1, 4817

How to compute the divisors of 4817?

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 4817 by each of the numbers from 1 to 4817 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)

4817 / 1 = 4817 (the remainder is 0, so 1 is a divisor of 4817)
4817 / 2 = 2408.5 (the remainder is 1, so 2 is not a divisor of 4817)
4817 / 3 = 1605.6666666667 (the remainder is 2, so 3 is not a divisor of 4817)
...
4817 / 4816 = 1.000207641196 (the remainder is 1, so 4816 is not a divisor of 4817)
4817 / 4817 = 1 (the remainder is 0, so 4817 is a divisor of 4817)

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 4817 (i.e. 69.404610797843). 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 $\frac{N}{d} = D$ )

4817 / 1 = 4817 (the remainder is 0, so 1 and 4817 are divisors of 4817)
4817 / 2 = 2408.5 (the remainder is 1, so 2 is not a divisor of 4817)
4817 / 3 = 1605.6666666667 (the remainder is 2, so 3 is not a divisor of 4817)
...
4817 / 68 = 70.838235294118 (the remainder is 57, so 68 is not a divisor of 4817)
4817 / 69 = 69.811594202899 (the remainder is 56, so 69 is not a divisor of 4817)