What are the divisors of 4319?

1, 7, 617, 4319

There is a total of 4 positive divisors.
The sum of these divisors is 4944.
The arithmetic mean is 1236.

4 odd divisors

1, 7, 617, 4319

How to compute the divisors of 4319?

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 4319 by each of the numbers from 1 to 4319 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)

4319 / 1 = 4319 (the remainder is 0, so 1 is a divisor of 4319)
4319 / 2 = 2159.5 (the remainder is 1, so 2 is not a divisor of 4319)
4319 / 3 = 1439.6666666667 (the remainder is 2, so 3 is not a divisor of 4319)
...
4319 / 4318 = 1.0002315886985 (the remainder is 1, so 4318 is not a divisor of 4319)
4319 / 4319 = 1 (the remainder is 0, so 4319 is a divisor of 4319)

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 4319 (i.e. 65.719099202591). 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 $\frac{N}{d} = D$ )

4319 / 1 = 4319 (the remainder is 0, so 1 and 4319 are divisors of 4319)
4319 / 2 = 2159.5 (the remainder is 1, so 2 is not a divisor of 4319)
4319 / 3 = 1439.6666666667 (the remainder is 2, so 3 is not a divisor of 4319)
...
4319 / 64 = 67.484375 (the remainder is 31, so 64 is not a divisor of 4319)
4319 / 65 = 66.446153846154 (the remainder is 29, so 65 is not a divisor of 4319)