What are the divisors of 212?

1, 2, 4, 53, 106, 212

There is a total of 6 positive divisors.
The sum of these divisors is 378.
The arithmetic mean is 63.

4 even divisors

2, 4, 106, 212

2 odd divisors

1, 53

How to compute the divisors of 212?

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 212 by each of the numbers from 1 to 212 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)

212 / 1 = 212 (the remainder is 0, so 1 is a divisor of 212)
212 / 2 = 106 (the remainder is 0, so 2 is a divisor of 212)
212 / 3 = 70.666666666667 (the remainder is 2, so 3 is not a divisor of 212)
...
212 / 211 = 1.0047393364929 (the remainder is 1, so 211 is not a divisor of 212)
212 / 212 = 1 (the remainder is 0, so 212 is a divisor of 212)

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 212 (i.e. 14.560219778561). 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 $\frac{N}{d} = D$ )

212 / 1 = 212 (the remainder is 0, so 1 and 212 are divisors of 212)
212 / 2 = 106 (the remainder is 0, so 2 and 106 are divisors of 212)
212 / 3 = 70.666666666667 (the remainder is 2, so 3 is not a divisor of 212)
...
212 / 13 = 16.307692307692 (the remainder is 4, so 13 is not a divisor of 212)
212 / 14 = 15.142857142857 (the remainder is 2, so 14 is not a divisor of 212)