What are the divisors of 4315?

1, 5, 863, 4315

There is a total of 4 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 1296.

4 odd divisors

1, 5, 863, 4315

How to compute the divisors of 4315?

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 4315 by each of the numbers from 1 to 4315 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)

4315 / 1 = 4315 (the remainder is 0, so 1 is a divisor of 4315)
4315 / 2 = 2157.5 (the remainder is 1, so 2 is not a divisor of 4315)
4315 / 3 = 1438.3333333333 (the remainder is 1, so 3 is not a divisor of 4315)
...
4315 / 4314 = 1.0002318034307 (the remainder is 1, so 4314 is not a divisor of 4315)
4315 / 4315 = 1 (the remainder is 0, so 4315 is a divisor of 4315)

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 4315 (i.e. 65.68865959966). 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 $\frac{N}{d} = D$ )

4315 / 1 = 4315 (the remainder is 0, so 1 and 4315 are divisors of 4315)
4315 / 2 = 2157.5 (the remainder is 1, so 2 is not a divisor of 4315)
4315 / 3 = 1438.3333333333 (the remainder is 1, so 3 is not a divisor of 4315)
...
4315 / 64 = 67.421875 (the remainder is 27, so 64 is not a divisor of 4315)
4315 / 65 = 66.384615384615 (the remainder is 25, so 65 is not a divisor of 4315)