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Find the prime factorization of each number by using a factor tree.

[tex]$440 = 2 \times 2 \times$[/tex]

(a) 24
(b) 36
(c) 210
(d) 180
(e) 300

Sagot :

GinnyAnswer
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]
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