Questions: Write 48 as a product of prime factors. 48= ×

Transcript text: Write 48 as a product of prime factors. \[ 48= \] $\square$ $\times \square$

Solution

Step 1: Find the Smallest Prime Factor

The smallest prime number is 2. Check if 48 is divisible by 2. Since 48 is even, it is divisible by 2.

\[ 48 \div 2 = 24 \]

Step 2: Continue Factoring

Now, take the result, 24, and check if it is divisible by 2. Since 24 is also even, divide by 2 again.

\[ 24 \div 2 = 12 \]

Step 3: Continue Factoring

Take the result, 12, and check if it is divisible by 2. Since 12 is even, divide by 2 again.

\[ 12 \div 2 = 6 \]

Step 4: Continue Factoring

Take the result, 6, and check if it is divisible by 2. Since 6 is even, divide by 2 again.

\[ 6 \div 2 = 3 \]

Step 5: Final Prime Factor

Now, take the result, 3, which is a prime number. Therefore, the factorization process stops here.

The prime factorization of 48 is:

\[ 48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3 \]

\[ \boxed{48 = 2^4 \times 3} \]

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