What are the divisors of 4155?

1, 3, 5, 15, 277, 831, 1385, 4155

There is a total of 8 positive divisors.
The sum of these divisors is 6672.
The arithmetic mean is 834.

8 odd divisors

1, 3, 5, 15, 277, 831, 1385, 4155

How to compute the divisors of 4155?

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 4155 by each of the numbers from 1 to 4155 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)

4155 / 1 = 4155 (the remainder is 0, so 1 is a divisor of 4155)
4155 / 2 = 2077.5 (the remainder is 1, so 2 is not a divisor of 4155)
4155 / 3 = 1385 (the remainder is 0, so 3 is a divisor of 4155)
...
4155 / 4154 = 1.0002407318247 (the remainder is 1, so 4154 is not a divisor of 4155)
4155 / 4155 = 1 (the remainder is 0, so 4155 is a divisor of 4155)

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 4155 (i.e. 64.459289477933). 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 $\frac{N}{d} = D$ )

4155 / 1 = 4155 (the remainder is 0, so 1 and 4155 are divisors of 4155)
4155 / 2 = 2077.5 (the remainder is 1, so 2 is not a divisor of 4155)
4155 / 3 = 1385 (the remainder is 0, so 3 and 1385 are divisors of 4155)
...
4155 / 63 = 65.952380952381 (the remainder is 60, so 63 is not a divisor of 4155)
4155 / 64 = 64.921875 (the remainder is 59, so 64 is not a divisor of 4155)