What are the divisors of 4179?

1, 3, 7, 21, 199, 597, 1393, 4179

There is a total of 8 positive divisors.
The sum of these divisors is 6400.
The arithmetic mean is 800.

8 odd divisors

1, 3, 7, 21, 199, 597, 1393, 4179

How to compute the divisors of 4179?

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 4179 by each of the numbers from 1 to 4179 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)

4179 / 1 = 4179 (the remainder is 0, so 1 is a divisor of 4179)
4179 / 2 = 2089.5 (the remainder is 1, so 2 is not a divisor of 4179)
4179 / 3 = 1393 (the remainder is 0, so 3 is a divisor of 4179)
...
4179 / 4178 = 1.0002393489708 (the remainder is 1, so 4178 is not a divisor of 4179)
4179 / 4179 = 1 (the remainder is 0, so 4179 is a divisor of 4179)

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 4179 (i.e. 64.645185435576). 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 $\frac{N}{d} = D$ )

4179 / 1 = 4179 (the remainder is 0, so 1 and 4179 are divisors of 4179)
4179 / 2 = 2089.5 (the remainder is 1, so 2 is not a divisor of 4179)
4179 / 3 = 1393 (the remainder is 0, so 3 and 1393 are divisors of 4179)
...
4179 / 63 = 66.333333333333 (the remainder is 21, so 63 is not a divisor of 4179)
4179 / 64 = 65.296875 (the remainder is 19, so 64 is not a divisor of 4179)