What are the divisors of 4295?

1, 5, 859, 4295

There is a total of 4 positive divisors.
The sum of these divisors is 5160.
The arithmetic mean is 1290.

4 odd divisors

1, 5, 859, 4295

How to compute the divisors of 4295?

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 4295 by each of the numbers from 1 to 4295 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)

4295 / 1 = 4295 (the remainder is 0, so 1 is a divisor of 4295)
4295 / 2 = 2147.5 (the remainder is 1, so 2 is not a divisor of 4295)
4295 / 3 = 1431.6666666667 (the remainder is 2, so 3 is not a divisor of 4295)
...
4295 / 4294 = 1.0002328830927 (the remainder is 1, so 4294 is not a divisor of 4295)
4295 / 4295 = 1 (the remainder is 0, so 4295 is a divisor of 4295)

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 4295 (i.e. 65.536249511244). 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 $\frac{N}{d} = D$ )

4295 / 1 = 4295 (the remainder is 0, so 1 and 4295 are divisors of 4295)
4295 / 2 = 2147.5 (the remainder is 1, so 2 is not a divisor of 4295)
4295 / 3 = 1431.6666666667 (the remainder is 2, so 3 is not a divisor of 4295)
...
4295 / 64 = 67.109375 (the remainder is 7, so 64 is not a divisor of 4295)
4295 / 65 = 66.076923076923 (the remainder is 5, so 65 is not a divisor of 4295)