What are the divisors of 4215?

1, 3, 5, 15, 281, 843, 1405, 4215

There is a total of 8 positive divisors.
The sum of these divisors is 6768.
The arithmetic mean is 846.

8 odd divisors

1, 3, 5, 15, 281, 843, 1405, 4215

How to compute the divisors of 4215?

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 4215 by each of the numbers from 1 to 4215 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)

4215 / 1 = 4215 (the remainder is 0, so 1 is a divisor of 4215)
4215 / 2 = 2107.5 (the remainder is 1, so 2 is not a divisor of 4215)
4215 / 3 = 1405 (the remainder is 0, so 3 is a divisor of 4215)
...
4215 / 4214 = 1.000237304224 (the remainder is 1, so 4214 is not a divisor of 4215)
4215 / 4215 = 1 (the remainder is 0, so 4215 is a divisor of 4215)

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 4215 (i.e. 64.923031352518). 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 $\frac{N}{d} = D$ )

4215 / 1 = 4215 (the remainder is 0, so 1 and 4215 are divisors of 4215)
4215 / 2 = 2107.5 (the remainder is 1, so 2 is not a divisor of 4215)
4215 / 3 = 1405 (the remainder is 0, so 3 and 1405 are divisors of 4215)
...
4215 / 63 = 66.904761904762 (the remainder is 57, so 63 is not a divisor of 4215)
4215 / 64 = 65.859375 (the remainder is 55, so 64 is not a divisor of 4215)