What are the divisors of 4289?

1, 4289

There is a total of 2 positive divisors.
The sum of these divisors is 4290.
The arithmetic mean is 2145.

2 odd divisors

1, 4289

How to compute the divisors of 4289?

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 4289 by each of the numbers from 1 to 4289 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)

4289 / 1 = 4289 (the remainder is 0, so 1 is a divisor of 4289)
4289 / 2 = 2144.5 (the remainder is 1, so 2 is not a divisor of 4289)
4289 / 3 = 1429.6666666667 (the remainder is 2, so 3 is not a divisor of 4289)
...
4289 / 4288 = 1.0002332089552 (the remainder is 1, so 4288 is not a divisor of 4289)
4289 / 4289 = 1 (the remainder is 0, so 4289 is a divisor of 4289)

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 4289 (i.e. 65.490457320132). 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 $\frac{N}{d} = D$ )

4289 / 1 = 4289 (the remainder is 0, so 1 and 4289 are divisors of 4289)
4289 / 2 = 2144.5 (the remainder is 1, so 2 is not a divisor of 4289)
4289 / 3 = 1429.6666666667 (the remainder is 2, so 3 is not a divisor of 4289)
...
4289 / 64 = 67.015625 (the remainder is 1, so 64 is not a divisor of 4289)
4289 / 65 = 65.984615384615 (the remainder is 64, so 65 is not a divisor of 4289)