What are the divisors of 4217?

1, 4217

There is a total of 2 positive divisors.
The sum of these divisors is 4218.
The arithmetic mean is 2109.

2 odd divisors

1, 4217

How to compute the divisors of 4217?

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 4217 by each of the numbers from 1 to 4217 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)

4217 / 1 = 4217 (the remainder is 0, so 1 is a divisor of 4217)
4217 / 2 = 2108.5 (the remainder is 1, so 2 is not a divisor of 4217)
4217 / 3 = 1405.6666666667 (the remainder is 2, so 3 is not a divisor of 4217)
...
4217 / 4216 = 1.0002371916509 (the remainder is 1, so 4216 is not a divisor of 4217)
4217 / 4217 = 1 (the remainder is 0, so 4217 is a divisor of 4217)

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 4217 (i.e. 64.938432380217). 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 $\frac{N}{d} = D$ )

4217 / 1 = 4217 (the remainder is 0, so 1 and 4217 are divisors of 4217)
4217 / 2 = 2108.5 (the remainder is 1, so 2 is not a divisor of 4217)
4217 / 3 = 1405.6666666667 (the remainder is 2, so 3 is not a divisor of 4217)
...
4217 / 63 = 66.936507936508 (the remainder is 59, so 63 is not a divisor of 4217)
4217 / 64 = 65.890625 (the remainder is 57, so 64 is not a divisor of 4217)