What are the divisors of 4709?

1, 17, 277, 4709

There is a total of 4 positive divisors.
The sum of these divisors is 5004.
The arithmetic mean is 1251.

4 odd divisors

1, 17, 277, 4709

How to compute the divisors of 4709?

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 4709 by each of the numbers from 1 to 4709 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)

4709 / 1 = 4709 (the remainder is 0, so 1 is a divisor of 4709)
4709 / 2 = 2354.5 (the remainder is 1, so 2 is not a divisor of 4709)
4709 / 3 = 1569.6666666667 (the remainder is 2, so 3 is not a divisor of 4709)
...
4709 / 4708 = 1.000212404418 (the remainder is 1, so 4708 is not a divisor of 4709)
4709 / 4709 = 1 (the remainder is 0, so 4709 is a divisor of 4709)

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 4709 (i.e. 68.622153857191). 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 $\frac{N}{d} = D$ )

4709 / 1 = 4709 (the remainder is 0, so 1 and 4709 are divisors of 4709)
4709 / 2 = 2354.5 (the remainder is 1, so 2 is not a divisor of 4709)
4709 / 3 = 1569.6666666667 (the remainder is 2, so 3 is not a divisor of 4709)
...
4709 / 67 = 70.283582089552 (the remainder is 19, so 67 is not a divisor of 4709)
4709 / 68 = 69.25 (the remainder is 17, so 68 is not a divisor of 4709)