Let's find the prime factorization of each number using a factor tree:
### 1. Prime Factorization of 440
We start with the number 440:
[tex]\[
440 \div 2 = 220 \\
220 \div 2 = 110 \\
110 \div 2 = 55 \\
55 \div 5 = 11 \\
11 \div 11 = 1
\][/tex]
So, the prime factorization of 440 is:
[tex]\[
440 = 2^3 \times 5 \times 11
\][/tex]
### 2. Prime Factorization of 24
We start with the number 24:
[tex]\[
24 \div 2 = 12 \\
12 \div 2 = 6 \\
6 \div 2 = 3 \\
3 \div 3 = 1
\][/tex]
So, the prime factorization of 24 is:
[tex]\[
24 = 2^3 \times 3
\][/tex]
### 3. Prime Factorization of 36
We start with the number 36:
[tex]\[
36 \div 2 = 18 \\
18 \div 2 = 9 \\
9 \div 3 = 3 \\
3 \div 3 = 1
\][/tex]
So, the prime factorization of 36 is:
[tex]\[
36 = 2^2 \times 3^2
\][/tex]
### 4. Prime Factorization of 210
We start with the number 210:
[tex]\[
210 \div 2 = 105 \\
105 \div 3 = 35 \\
35 \div 5 = 7 \\
7 \div 7 = 1
\][/tex]
So, the prime factorization of 210 is:
[tex]\[
210 = 2 \times 3 \times 5 \times 7
\][/tex]
### 5. Prime Factorization of 180
We start with the number 180:
[tex]\[
180 \div 2 = 90 \\
90 \div 2 = 45 \\
45 \div 3 = 15 \\
15 \div 3 = 5 \\
5 \div 5 = 1
\][/tex]
So, the prime factorization of 180 is:
[tex]\[
180 = 2^2 \times 3^2 \times 5
\][/tex]
### 6. Prime Factorization of 300
We start with the number 300:
[tex]\[
300 \div 2 = 150 \\
150 \div 2 = 75 \\
75 \div 3 = 25 \\
25 \div 5 = 5 \\
5 \div 5 = 1
\][/tex]
So, the prime factorization of 300 is:
[tex]\[
300 = 2^2 \times 3 \times 5^2
\][/tex]
In summary, the prime factorizations are:
- [tex]\( 440 = 2^3 \times 5 \times 11 \)[/tex]
- [tex]\( 24 = 2^3 \times 3 \)[/tex]
- [tex]\( 36 = 2^2 \times 3^2 \)[/tex]
- [tex]\( 210 = 2 \times 3 \times 5 \times 7 \)[/tex]
- [tex]\( 180 = 2^2 \times 3^2 \times 5 \)[/tex]
- [tex]\( 300 = 2^2 \times 3 \times 5^2 \)[/tex]
