What are the divisors of 3212?

1, 2, 4, 11, 22, 44, 73, 146, 292, 803, 1606, 3212

There is a total of 12 positive divisors.
The sum of these divisors is 6216.
The arithmetic mean is 518.

8 even divisors

2, 4, 22, 44, 146, 292, 1606, 3212

4 odd divisors

1, 11, 73, 803

How to compute the divisors of 3212?

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 3212 by each of the numbers from 1 to 3212 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)

3212 / 1 = 3212 (the remainder is 0, so 1 is a divisor of 3212)
3212 / 2 = 1606 (the remainder is 0, so 2 is a divisor of 3212)
3212 / 3 = 1070.6666666667 (the remainder is 2, so 3 is not a divisor of 3212)
...
3212 / 3211 = 1.0003114294612 (the remainder is 1, so 3211 is not a divisor of 3212)
3212 / 3212 = 1 (the remainder is 0, so 3212 is a divisor of 3212)

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 3212 (i.e. 56.674509261219). 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 $\frac{N}{d} = D$ )

3212 / 1 = 3212 (the remainder is 0, so 1 and 3212 are divisors of 3212)
3212 / 2 = 1606 (the remainder is 0, so 2 and 1606 are divisors of 3212)
3212 / 3 = 1070.6666666667 (the remainder is 2, so 3 is not a divisor of 3212)
...
3212 / 55 = 58.4 (the remainder is 22, so 55 is not a divisor of 3212)
3212 / 56 = 57.357142857143 (the remainder is 20, so 56 is not a divisor of 3212)