What are the divisors of 4346?

1, 2, 41, 53, 82, 106, 2173, 4346

There is a total of 8 positive divisors.
The sum of these divisors is 6804.
The arithmetic mean is 850.5.

4 even divisors

2, 82, 106, 4346

4 odd divisors

1, 41, 53, 2173

How to compute the divisors of 4346?

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 4346 by each of the numbers from 1 to 4346 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)

4346 / 1 = 4346 (the remainder is 0, so 1 is a divisor of 4346)
4346 / 2 = 2173 (the remainder is 0, so 2 is a divisor of 4346)
4346 / 3 = 1448.6666666667 (the remainder is 2, so 3 is not a divisor of 4346)
...
4346 / 4345 = 1.0002301495972 (the remainder is 1, so 4345 is not a divisor of 4346)
4346 / 4346 = 1 (the remainder is 0, so 4346 is a divisor of 4346)

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 4346 (i.e. 65.924198895398). 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 $\frac{N}{d} = D$ )

4346 / 1 = 4346 (the remainder is 0, so 1 and 4346 are divisors of 4346)
4346 / 2 = 2173 (the remainder is 0, so 2 and 2173 are divisors of 4346)
4346 / 3 = 1448.6666666667 (the remainder is 2, so 3 is not a divisor of 4346)
...
4346 / 64 = 67.90625 (the remainder is 58, so 64 is not a divisor of 4346)
4346 / 65 = 66.861538461538 (the remainder is 56, so 65 is not a divisor of 4346)