What are the divisors of 4279?

1, 11, 389, 4279

There is a total of 4 positive divisors.
The sum of these divisors is 4680.
The arithmetic mean is 1170.

4 odd divisors

1, 11, 389, 4279

How to compute the divisors of 4279?

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 4279 by each of the numbers from 1 to 4279 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)

4279 / 1 = 4279 (the remainder is 0, so 1 is a divisor of 4279)
4279 / 2 = 2139.5 (the remainder is 1, so 2 is not a divisor of 4279)
4279 / 3 = 1426.3333333333 (the remainder is 1, so 3 is not a divisor of 4279)
...
4279 / 4278 = 1.0002337540907 (the remainder is 1, so 4278 is not a divisor of 4279)
4279 / 4279 = 1 (the remainder is 0, so 4279 is a divisor of 4279)

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 4279 (i.e. 65.414065765705). 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 $\frac{N}{d} = D$ )

4279 / 1 = 4279 (the remainder is 0, so 1 and 4279 are divisors of 4279)
4279 / 2 = 2139.5 (the remainder is 1, so 2 is not a divisor of 4279)
4279 / 3 = 1426.3333333333 (the remainder is 1, so 3 is not a divisor of 4279)
...
4279 / 64 = 66.859375 (the remainder is 55, so 64 is not a divisor of 4279)
4279 / 65 = 65.830769230769 (the remainder is 54, so 65 is not a divisor of 4279)