What are the divisors of 4306?

1, 2, 2153, 4306

There is a total of 4 positive divisors.
The sum of these divisors is 6462.
The arithmetic mean is 1615.5.

2 even divisors

2, 4306

2 odd divisors

1, 2153

How to compute the divisors of 4306?

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 4306 by each of the numbers from 1 to 4306 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)

4306 / 1 = 4306 (the remainder is 0, so 1 is a divisor of 4306)
4306 / 2 = 2153 (the remainder is 0, so 2 is a divisor of 4306)
4306 / 3 = 1435.3333333333 (the remainder is 1, so 3 is not a divisor of 4306)
...
4306 / 4305 = 1.0002322880372 (the remainder is 1, so 4305 is not a divisor of 4306)
4306 / 4306 = 1 (the remainder is 0, so 4306 is a divisor of 4306)

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 4306 (i.e. 65.620118866092). 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 $\frac{N}{d} = D$ )

4306 / 1 = 4306 (the remainder is 0, so 1 and 4306 are divisors of 4306)
4306 / 2 = 2153 (the remainder is 0, so 2 and 2153 are divisors of 4306)
4306 / 3 = 1435.3333333333 (the remainder is 1, so 3 is not a divisor of 4306)
...
4306 / 64 = 67.28125 (the remainder is 18, so 64 is not a divisor of 4306)
4306 / 65 = 66.246153846154 (the remainder is 16, so 65 is not a divisor of 4306)