Step 1: Prime factorise 216. Step 2: Find the GCF of 8 and 6. Step 3: Find the LCM of 12 and 18. Step 4: Find how many triangular numbers will form a sum of 36.

We find the prime factors of 216 by dividing it by the smallest prime numbers.

So, the prime factors of 216 are $2 \times 2 \times 2 \times 3 \times 3 \times 3$.
In exponential form, this is $2^3 \times 3^3$.
In set notation, the prime factors are the unique prime numbers involved.
The prime factors of 216 are $\boxed{\{2, 3\}}$.

First, list the factors for each number.
Factors of 8: 1, 2, 4, 8
Factors of 6: 1, 2, 3, 6
The common factors are 1 and 2. The greatest common factor (GCF) is the largest of these common factors.
The GCF of 8 and 6 is $\boxed{2}$.

We can find the LCM by listing multiples or using prime factorization.
Using prime factorization:
Prime factors of 12: $2^2 \times 3^1$
Prime factors of 18: $2^1 \times 3^2$
To find the LCM, we take the highest power of each prime factor present in either number.
LCM = $2^2 \times 3^2 = 4 \times 9 = 36$.
The LCM of 12 and 18 is $\boxed{36}$.

Triangular numbers are generated by the formula $T_n = \frac{n(n+1)}{2}$.
Let's list the first few triangular numbers:
$T_1 = \frac{1(1+1)}{2} = 1$
$T_2 = \frac{2(2+1)}{2} = 3$
$T_3 = \frac{3(3+1)}{2} = 6$
$T_4 = \frac{4(4+1)}{2} = 10$
$T_5 = \frac{5(5+1)}{2} = 15$
$T_6 = \frac{6(6+1)}{2} = 21$
$T_7 = \frac{7(7+1)}{2} = 28$
$T_8 = \frac{8(8+1)}{2} = 36$
The 8th triangular number is 36. Therefore, one triangular number (the 8th one) forms a sum of 36.
The number of triangular numbers is $\boxed{1}$.

i) 5, 10, 15, 20, 25, 30, ___, 40, 45, 50
This is an arithmetic sequence where each term increases by 5.
The next number after 30 is $30 + 5 = 35$.
The sequence is 5, 10, 15, 20, 25, 30, $\boxed{35}$, 40, 45, 50.

ii) 1, 3, ___, 7, 9, ___
This is an arithmetic sequence of odd numbers, where each term increases by 2.
The number after 3 is $3 + 2 = 5$.
The number after 9 is $9 + 2 = 11$.
The sequence is 1, 3, $\boxed{5}$, 7, 9, $\boxed{11}$.

iii) 1, 4, 9, 16, 25, ___
This sequence consists of perfect squares: $1^2, 2^2, 3^2, 4^2, 5^2$.
The next term in the sequence will be $6^2$.
$6^2 = 36$.
The sequence is 1, 4, 9, 16, 25, $\boxed{36}$.