What are the divisors of 4717?

1, 53, 89, 4717

There is a total of 4 positive divisors.
The sum of these divisors is 4860.
The arithmetic mean is 1215.

4 odd divisors

1, 53, 89, 4717

How to compute the divisors of 4717?

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 4717 by each of the numbers from 1 to 4717 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)

4717 / 1 = 4717 (the remainder is 0, so 1 is a divisor of 4717)
4717 / 2 = 2358.5 (the remainder is 1, so 2 is not a divisor of 4717)
4717 / 3 = 1572.3333333333 (the remainder is 1, so 3 is not a divisor of 4717)
...
4717 / 4716 = 1.0002120441052 (the remainder is 1, so 4716 is not a divisor of 4717)
4717 / 4717 = 1 (the remainder is 0, so 4717 is a divisor of 4717)

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 4717 (i.e. 68.680419334771). 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 $\frac{N}{d} = D$ )

4717 / 1 = 4717 (the remainder is 0, so 1 and 4717 are divisors of 4717)
4717 / 2 = 2358.5 (the remainder is 1, so 2 is not a divisor of 4717)
4717 / 3 = 1572.3333333333 (the remainder is 1, so 3 is not a divisor of 4717)
...
4717 / 67 = 70.402985074627 (the remainder is 27, so 67 is not a divisor of 4717)
4717 / 68 = 69.367647058824 (the remainder is 25, so 68 is not a divisor of 4717)