Prime Factorization practice worksheet for finding prime factors of numbers.

To solve the problem of finding the prime factorization for each number listed, we need to break down each number into its prime factors. Let's go through each number step by step.

Prime Factorization Steps:

1. Start with the smallest prime number (2) and divide the given number as many times as possible.
2. Move to the next smallest prime number (3) and continue dividing.
3. Repeat this process with subsequent prime numbers (5, 7, 11, etc.) until the quotient is 1.
4. Write the prime factors in ascending order.

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Solutions:

#### A) 9
- Divide by 3: \( 9 \div 3 = 3 \)
- Divide by 3 again: \( 3 \div 3 = 1 \)
- Prime factorization: \( 9 = 3 \times 3 \)

#### B) 16
- Divide by 2: \( 16 \div 2 = 8 \)
- Divide by 2: \( 8 \div 2 = 4 \)
- Divide by 2: \( 4 \div 2 = 2 \)
- Divide by 2: \( 2 \div 2 = 1 \)
- Prime factorization: \( 16 = 2 \times 2 \times 2 \times 2 \)

#### C) 28
- Divide by 2: \( 28 \div 2 = 14 \)
- Divide by 2: \( 14 \div 2 = 7 \)
- Divide by 7: \( 7 \div 7 = 1 \)
- Prime factorization: \( 28 = 2 \times 2 \times 7 \)

#### D) 36
- Divide by 2: \( 36 \div 2 = 18 \)
- Divide by 2: \( 18 \div 2 = 9 \)
- Divide by 3: \( 9 \div 3 = 3 \)
- Divide by 3: \( 3 \div 3 = 1 \)
- Prime factorization: \( 36 = 2 \times 2 \times 3 \times 3 \)

#### E) 42
- Divide by 2: \( 42 \div 2 = 21 \)
- Divide by 3: \( 21 \div 3 = 7 \)
- Divide by 7: \( 7 \div 7 = 1 \)
- Prime factorization: \( 42 = 2 \times 3 \times 7 \)

#### F) 60
- Divide by 2: \( 60 \div 2 = 30 \)
- Divide by 2: \( 30 \div 2 = 15 \)
- Divide by 3: \( 15 \div 3 = 5 \)
- Divide by 5: \( 5 \div 5 = 1 \)
- Prime factorization: \( 60 = 2 \times 2 \times 3 \times 5 \)

#### G) 74
- Divide by 2: \( 74 \div 2 = 37 \)
- Divide by 37: \( 37 \div 37 = 1 \)
- Prime factorization: \( 74 = 2 \times 37 \)

#### H) 88
- Divide by 2: \( 88 \div 2 = 44 \)
- Divide by 2: \( 44 \div 2 = 22 \)
- Divide by 2: \( 22 \div 2 = 11 \)
- Divide by 11: \( 11 \div 11 = 1 \)
- Prime factorization: \( 88 = 2 \times 2 \times 2 \times 11 \)

#### I) 96
- Divide by 2: \( 96 \div 2 = 48 \)
- Divide by 2: \( 48 \div 2 = 24 \)
- Divide by 2: \( 24 \div 2 = 12 \)
- Divide by 2: \( 12 \div 2 = 6 \)
- Divide by 2: \( 6 \div 2 = 3 \)
- Divide by 3: \( 3 \div 3 = 1 \)
- Prime factorization: \( 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \)

#### J) 101
- 101 is a prime number (it has no divisors other than 1 and itself).
- Prime factorization: \( 101 = 101 \)

#### K) 124
- Divide by 2: \( 124 \div 2 = 62 \)
- Divide by 2: \( 62 \div 2 = 31 \)
- Divide by 31: \( 31 \div 31 = 1 \)
- Prime factorization: \( 124 = 2 \times 2 \times 31 \)

#### L) 195
- Divide by 3: \( 195 \div 3 = 65 \)
- Divide by 5: \( 65 \div 5 = 13 \)
- Divide by 13: \( 13 \div 13 = 1 \)
- Prime factorization: \( 195 = 3 \times 5 \times 13 \)

#### M) 244
- Divide by 2: \( 244 \div 2 = 122 \)
- Divide by 2: \( 122 \div 2 = 61 \)
- Divide by 61: \( 61 \div 61 = 1 \)
- Prime factorization: \( 244 = 2 \times 2 \times 61 \)

#### N) 393
- Divide by 3: \( 393 \div 3 = 131 \)
- Divide by 131: \( 131 \div 131 = 1 \)
- Prime factorization: \( 393 = 3 \times 131 \)

#### O) 450
- Divide by 2: \( 450 \div 2 = 225 \)
- Divide by 3: \( 225 \div 3 = 75 \)
- Divide by 3: \( 75 \div 3 = 25 \)
- Divide by 5: \( 25 \div 5 = 5 \)
- Divide by 5: \( 5 \div 5 = 1 \)
- Prime factorization: \( 450 = 2 \times 3 \times 3 \times 5 \times 5 \)

#### P) 629
- Divide by 17: \( 629 \div 17 = 37 \)
- Divide by 37: \( 37 \div 37 = 1 \)
- Prime factorization: \( 629 = 17 \times 37 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{A) } 9 & 3 \times 3 \\
\text{B) } 16 & 2 \times 2 \times 2 \times 2 \\
\text{C) } 28 & 2 \times 2 \times 7 \\
\text{D) } 36 & 2 \times 2 \times 3 \times 3 \\
\text{E) } 42 & 2 \times 3 \times 7 \\
\text{F) } 60 & 2 \times 2 \times 3 \times 5 \\
\text{G) } 74 & 2 \times 37 \\
\text{H) } 88 & 2 \times 2 \times 2 \times 11 \\
\text{I) } 96 & 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\
\text{J) } 101 & 101 \\
\text{K) } 124 & 2 \times 2 \times 31 \\
\text{L) } 195 & 3 \times 5 \times 13 \\
\text{M) } 244 & 2 \times 2 \times 61 \\
\text{N) } 393 & 3 \times 131 \\
\text{O) } 450 & 2 \times 3 \times 3 \times 5 \times 5 \\
\text{P) } 629 & 17 \times 37 \\
\end{array}
}
\]