What are the divisors of 4351?

1, 19, 229, 4351

There is a total of 4 positive divisors.
The sum of these divisors is 4600.
The arithmetic mean is 1150.

4 odd divisors

1, 19, 229, 4351

How to compute the divisors of 4351?

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 4351 by each of the numbers from 1 to 4351 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)

4351 / 1 = 4351 (the remainder is 0, so 1 is a divisor of 4351)
4351 / 2 = 2175.5 (the remainder is 1, so 2 is not a divisor of 4351)
4351 / 3 = 1450.3333333333 (the remainder is 1, so 3 is not a divisor of 4351)
...
4351 / 4350 = 1.0002298850575 (the remainder is 1, so 4350 is not a divisor of 4351)
4351 / 4351 = 1 (the remainder is 0, so 4351 is a divisor of 4351)

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 4351 (i.e. 65.962110336162). 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 $\frac{N}{d} = D$ )

4351 / 1 = 4351 (the remainder is 0, so 1 and 4351 are divisors of 4351)
4351 / 2 = 2175.5 (the remainder is 1, so 2 is not a divisor of 4351)
4351 / 3 = 1450.3333333333 (the remainder is 1, so 3 is not a divisor of 4351)
...
4351 / 64 = 67.984375 (the remainder is 63, so 64 is not a divisor of 4351)
4351 / 65 = 66.938461538462 (the remainder is 61, so 65 is not a divisor of 4351)