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Extracted Problems and Solutions:

1. Problem 1:

   • Complete the table by calculating the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of the given numbers.

   a	b	GCF(a, b)	LCM(a, b)
   24	36
   15	25
   9	12

   Solution:

   • For $a = 24$, $b = 36$:
     • GCF(24, 36) = 12
     • LCM(24, 36) = 72
   • For $a = 15$, $b = 25$:
     • GCF(15, 25) = 5
     • LCM(15, 25) = 75
   • For $a = 9$, $b = 12$:
     • GCF(9, 12) = 3
     • LCM(9, 12) = 36

   The completed table:

   a	b	GCF(a, b)	LCM(a, b)
   24	36	12	72
   15	25	5	75
   9	12	3	36

2. Problem 2:

   • Find the prime factorization of each number.

   Solution:

   • $20 = 2^2 \times 5$
   • $35 = 5 \times 7$
   • $42 = 2 \times 3 \times 7$
   • $60 = 2^2 \times 3 \times 5$

3. Problem 3:

   • Evaluate whether the following numbers are prime or composite.
     • $2$
     • $9$
     • $17$
     • $51$

   Solution:

   • $2$ is a prime number.
   • $9$ is a composite number.
   • $17$ is a prime number.
   • $51$ is a composite number.

4. Problem 4:

   • Express the following as a product of prime factors:
     • $18$
     • $24$
     • $40$
     • $84$

   Solution:

   • $18 = 2 \times 3^2$
   • $24 = 2^3 \times 3$
   • $40 = 2^3 \times 5$
   • $84 = 2^2 \times 3 \times 7$

5. Problem 5:

   • Fill in the missing values in the table based on the highest common factor (HCF) and the least common multiple (LCM).

   Solution:

   • Without the specific table, I can’t fill in exact values. If you provide the missing values or clarify, I can assist further.

Would you like more details or explanations for any of the above problems?

Here are some related questions you might be interested in:

1. How do you calculate the GCF and LCM of two numbers?
2. What are some real-life applications of prime factorization?
3. How can you determine if a number is prime or composite?
4. Why is the prime factorization of a number unique?
5. How does the LCM of two numbers relate to their GCF?

Tip: Understanding the relationship between GCF and LCM can help solve problems involving fractions, ratios, and real-world scenarios efficiently.