Find the prime factorization for each number below.  

1. $36$ 

   Hint (a):

   The first few prime numbers are: $2, 3, 5, 7, 11$, and $13$.

   More Help (a):

   Start by dividing the number with the lowest prime number.
   $36 ÷ 2 = 18$
   Now divide $18$ by another prime number, and continue until the number is no longer divisible.

   Answer (a):

   $2^{2}\cdot 3^{2}$

2. $45$ 

   Hint (b):

   See part (a).

3. Find the greatest common factor for $36$ and $45$.

   Hint (c):

   Write out the factors for $36$ and $45$.
   $36: 1, 2, 3, 4, 6, 9, 12, 18, \text{and } 36.$
   $45: 1, 3, 5, 9, 15, \text{and } 45.$

   More Help (c):

   Which common factor is the greatest?

4. Find the least common multiple for $36$ and $45$.

   Hint (d):

   Write out the multiples for $36$ and $45$.
   It has been started below.
   $36: 36, 72, 108...$
   $45: 45, 90, 135...$