What are the divisors of 4297?

1, 4297

There is a total of 2 positive divisors.
The sum of these divisors is 4298.
The arithmetic mean is 2149.

2 odd divisors

1, 4297

How to compute the divisors of 4297?

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 4297 by each of the numbers from 1 to 4297 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)

4297 / 1 = 4297 (the remainder is 0, so 1 is a divisor of 4297)
4297 / 2 = 2148.5 (the remainder is 1, so 2 is not a divisor of 4297)
4297 / 3 = 1432.3333333333 (the remainder is 1, so 3 is not a divisor of 4297)
...
4297 / 4296 = 1.0002327746741 (the remainder is 1, so 4296 is not a divisor of 4297)
4297 / 4297 = 1 (the remainder is 0, so 4297 is a divisor of 4297)

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 4297 (i.e. 65.55150646629). 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 $\frac{N}{d} = D$ )

4297 / 1 = 4297 (the remainder is 0, so 1 and 4297 are divisors of 4297)
4297 / 2 = 2148.5 (the remainder is 1, so 2 is not a divisor of 4297)
4297 / 3 = 1432.3333333333 (the remainder is 1, so 3 is not a divisor of 4297)
...
4297 / 64 = 67.140625 (the remainder is 9, so 64 is not a divisor of 4297)
4297 / 65 = 66.107692307692 (the remainder is 7, so 65 is not a divisor of 4297)