What are the divisors of 4216?

1, 2, 4, 8, 17, 31, 34, 62, 68, 124, 136, 248, 527, 1054, 2108, 4216

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

12 even divisors

2, 4, 8, 34, 62, 68, 124, 136, 248, 1054, 2108, 4216

4 odd divisors

1, 17, 31, 527

How to compute the divisors of 4216?

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 4216 by each of the numbers from 1 to 4216 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)

4216 / 1 = 4216 (the remainder is 0, so 1 is a divisor of 4216)
4216 / 2 = 2108 (the remainder is 0, so 2 is a divisor of 4216)
4216 / 3 = 1405.3333333333 (the remainder is 1, so 3 is not a divisor of 4216)
...
4216 / 4215 = 1.0002372479241 (the remainder is 1, so 4215 is not a divisor of 4216)
4216 / 4216 = 1 (the remainder is 0, so 4216 is a divisor of 4216)

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 4216 (i.e. 64.930732322992). 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 $\frac{N}{d} = D$ )

4216 / 1 = 4216 (the remainder is 0, so 1 and 4216 are divisors of 4216)
4216 / 2 = 2108 (the remainder is 0, so 2 and 2108 are divisors of 4216)
4216 / 3 = 1405.3333333333 (the remainder is 1, so 3 is not a divisor of 4216)
...
4216 / 63 = 66.920634920635 (the remainder is 58, so 63 is not a divisor of 4216)
4216 / 64 = 65.875 (the remainder is 56, so 64 is not a divisor of 4216)