### Home > CC1 > Chapter 4 > Lesson 4.1.3 > Problem4-36

4-36.

Find the prime factorization for each number below.

1. $36$

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

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.

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

2. $45$

See part (a).

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

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

Which common factor is the greatest?

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

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