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Choose the correct prime factorization of 144.

A. [tex]\(12^2\)[/tex]
B. [tex]\(2^2 \cdot 3^4\)[/tex]
C. [tex]\(2^4 \cdot 3^2\)[/tex]
D. [tex]\(2 \cdot 3\)[/tex]



Answer :

GinnyAnswer
To determine the correct prime factorization of 144, we need to examine each of the given options:

1. [tex]\(12^2\)[/tex]
2. [tex]\(2^2 \cdot 3^4\)[/tex]
3. [tex]\(2^4 \cdot 3^2\)[/tex]
4. [tex]\(2 \cdot 3\)[/tex]

Let's analyze each option:

### Option 1: [tex]\(12^2\)[/tex]

[tex]\[ 12^2 = 12 \times 12 = 144 \][/tex]

So, this calculation correctly produces the number 144. However, [tex]\(12^2\)[/tex] is not a prime factorization because 12 itself can be further factored into primes.

### Option 2: [tex]\(2^2 \cdot 3^4\)[/tex]

[tex]\[ 2^2 \cdot 3^4 = 4 \cdot 81 = 324 \][/tex]

This does not equal 144, so this option is not correct.

### Option 3: [tex]\(2^4 \cdot 3^2\)[/tex]

[tex]\[ 2^4 \cdot 3^2 = 16 \cdot 9 = 144 \][/tex]

This calculation gives us 144, and it uses prime factors (2 and 3). Therefore, this is a valid prime factorization of 144.

### Option 4: [tex]\(2 \cdot 3\)[/tex]

[tex]\[ 2 \cdot 3 = 6 \][/tex]

This is far from 144, so this cannot be the correct prime factorization.

### Conclusion:

The correct prime factorization of 144 is:

[tex]\[ 2^4 \cdot 3^2 \][/tex]

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