Practice worksheet on finding factors and greatest common factors of numbers and algebraic expressions.

Actually, I can’t see or process images — including the one you uploaded. Since I’m a text-based AI, I don’t have access to visual content unless you describe it or paste the text from it.

However, looking at your message and the partial text you included (“Factors and Greatest Common Factor”, “State whether each number is prime or composite…”, etc.), I can tell this is a math worksheet on prime/composite numbers and greatest common factor (GCF).

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✔ Here’s how to solve the problems typically found on such a worksheet:

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## 🧮 Part 1: Prime or Composite?

Definitions:

- Prime number: A number >1 with exactly two factors: 1 and itself.
- Composite number: A number >1 with more than two factors.
- 1 is neither prime nor composite.

Example Problems (from your text):

Let’s assume these are the numbers listed (based on typical worksheets):

> 1. 10 → Composite (factors: 1, 2, 5, 10)
> 2. 13 → Prime (factors: 1, 13)
> 3. 22 → Composite (factors: 1, 2, 11, 22)
> 4. 29 → Prime (factors: 1, 29)
> 5. 36 → Composite (factors: 1, 2, 3, 4, 6, 9, 12, 18, 36)

✔️ Tip: Check divisibility by small primes (2, 3, 5, 7, 11). If divisible by any other than 1 and itself → composite.

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## 🔢 Part 2: Prime Factorization

Write each number as a product of prime numbers.

Examples:
> 10 = 2 × 5
> 13 = 13 (already prime)
> 22 = 2 × 11
> 29 = 29 (prime)
> 36 = 2 × 2 × 3 × 3 = 2² × 3²

✔️ Use factor trees or repeated division by primes.

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## 📐 Part 3: Factor Each Expression Completely (Algebraic)

You’ll see expressions like:
> 16x³y² → 2⁴ · x³ · y²
> 12a²b³c → 2² · 3 · a² · b³ · c

✔️ Break coefficients into prime factors, and leave variables with exponents.

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## 🤝 Part 4: Find the GCF of Given Monomials

Example:
> 24, 48, 60
→ Prime factorizations:
 24 = 2³ × 3
 48 = 2⁴ × 3
 60 = 2² × 3 × 5
→ GCF = lowest power of common primes = 2² × 3 = 12

Another example:
> 18x²y, 24xy², 30x³y
→ Coefficients: GCF(18,24,30) = 6
→ Variables: min exponent of x = x¹, min exponent of y = y¹
→ GCF = 6xy

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## ✔ Final Tips for This Worksheet:

1. For numbers 1–20, memorize which are prime:
 Primes ≤20: 2, 3, 5, 7, 11, 13, 17, 19
 Everything else (except 1) is composite.

2. For GCF of monomials:
 - Take GCF of coefficients
 - For each variable, take the smallest exponent present in all terms

3. Factor completely:
 - Don’t stop until everything is prime or fully broken down

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