What are the divisors of 3216?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 67, 134, 201, 268, 402, 536, 804, 1072, 1608, 3216

There is a total of 20 positive divisors.
The sum of these divisors is 8432.
The arithmetic mean is 421.6.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 134, 268, 402, 536, 804, 1072, 1608, 3216

4 odd divisors

1, 3, 67, 201

How to compute the divisors of 3216?

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 3216 by each of the numbers from 1 to 3216 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)

3216 / 1 = 3216 (the remainder is 0, so 1 is a divisor of 3216)
3216 / 2 = 1608 (the remainder is 0, so 2 is a divisor of 3216)
3216 / 3 = 1072 (the remainder is 0, so 3 is a divisor of 3216)
...
3216 / 3215 = 1.0003110419907 (the remainder is 1, so 3215 is not a divisor of 3216)
3216 / 3216 = 1 (the remainder is 0, so 3216 is a divisor of 3216)

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 3216 (i.e. 56.709787515031). 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 $\frac{N}{d} = D$ )

3216 / 1 = 3216 (the remainder is 0, so 1 and 3216 are divisors of 3216)
3216 / 2 = 1608 (the remainder is 0, so 2 and 1608 are divisors of 3216)
3216 / 3 = 1072 (the remainder is 0, so 3 and 1072 are divisors of 3216)
...
3216 / 55 = 58.472727272727 (the remainder is 26, so 55 is not a divisor of 3216)
3216 / 56 = 57.428571428571 (the remainder is 24, so 56 is not a divisor of 3216)