What are the divisors of 4729?

1, 4729

There is a total of 2 positive divisors.
The sum of these divisors is 4730.
The arithmetic mean is 2365.

2 odd divisors

1, 4729

How to compute the divisors of 4729?

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 4729 by each of the numbers from 1 to 4729 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)

4729 / 1 = 4729 (the remainder is 0, so 1 is a divisor of 4729)
4729 / 2 = 2364.5 (the remainder is 1, so 2 is not a divisor of 4729)
4729 / 3 = 1576.3333333333 (the remainder is 1, so 3 is not a divisor of 4729)
...
4729 / 4728 = 1.0002115059222 (the remainder is 1, so 4728 is not a divisor of 4729)
4729 / 4729 = 1 (the remainder is 0, so 4729 is a divisor of 4729)

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 4729 (i.e. 68.767724987817). 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 $\frac{N}{d} = D$ )

4729 / 1 = 4729 (the remainder is 0, so 1 and 4729 are divisors of 4729)
4729 / 2 = 2364.5 (the remainder is 1, so 2 is not a divisor of 4729)
4729 / 3 = 1576.3333333333 (the remainder is 1, so 3 is not a divisor of 4729)
...
4729 / 67 = 70.582089552239 (the remainder is 39, so 67 is not a divisor of 4729)
4729 / 68 = 69.544117647059 (the remainder is 37, so 68 is not a divisor of 4729)