8 Exercises to Master Prime and Composite Numbers

Mastering Prime and Composite Numbers: 8 Essential Exercises

Prime and composite numbers are fundamental concepts in number theory, and mastering them is crucial for success in mathematics and problem-solving. In this article, we will provide you with 8 exercises to help you improve your understanding and skills in working with prime and composite numbers.

Exercise 1: Identifying Prime Numbers

Instructions: Identify whether each of the following numbers is prime or composite.

• 23
• 34
• 47
• 56
• 67

Solution:

• 23: Prime
• 34: Composite (2 x 17)
• 47: Prime
• 56: Composite (2 x 2 x 2 x 7)
• 67: Prime

Exercise 2: Finding Prime Factors

Instructions: Find the prime factors of each of the following numbers.

• 12
• 24
• 36
• 48

Solution:

• 12: 2 x 2 x 3
• 24: 2 x 2 x 2 x 3
• 36: 2 x 2 x 3 x 3
• 48: 2 x 2 x 2 x 2 x 3

Exercise 3: Identifying Composite Numbers

Instructions: Identify whether each of the following numbers is composite.

• 25
• 37
• 49
• 63

Solution:

• 25: Composite (5 x 5)
• 37: Not composite (prime)
• 49: Composite (7 x 7)
• 63: Composite (3 x 3 x 7)

Exercise 4: Finding the Least Common Multiple (LCM)

Instructions: Find the LCM of each pair of numbers.

• 12 and 18
• 24 and 36
• 48 and 60

Solution:

• 12 and 18: 36
• 24 and 36: 72
• 48 and 60: 120

Exercise 5: Finding the Greatest Common Divisor (GCD)

Instructions: Find the GCD of each pair of numbers.

• 24 and 36
• 48 and 60
• 72 and 90

Solution:

• 24 and 36: 12
• 48 and 60: 12
• 72 and 90: 18

Exercise 6: Prime Number Patterns

Instructions: Identify the next prime number in each sequence.

• 2, 3, 5, 7, 11, ___
• 3, 5, 7, 11, 13, ___
• 5, 7, 11, 13, 17, ___

Solution:

• 2, 3, 5, 7, 11, 13
• 3, 5, 7, 11, 13, 17
• 5, 7, 11, 13, 17, 19

Exercise 7: Composite Number Patterns

Instructions: Identify the next composite number in each sequence.

• 4, 6, 8, 9, 10, ___
• 6, 8, 9, 10, 12, ___
• 9, 10, 12, 14, 15, ___

Solution:

• 4, 6, 8, 9, 10, 12
• 6, 8, 9, 10, 12, 14
• 9, 10, 12, 14, 15, 16

Exercise 8: Real-World Applications

Instructions: Solve the following real-world problems involving prime and composite numbers.

• A bookshelf has 12 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many prime numbers of books can be placed on the shelves?
• A bakery sells 24 cupcakes per hour. If they want to package the cupcakes in boxes of 4 or 6, how many boxes can they make in an hour?

Solution:

• Since 12 is a composite number, we need to find the prime factors of 12, which are 2 and 3. We can place 2 x 2 x 3 = 12 books on the shelves, but only 2, 3, and 5 are prime numbers, so we can place 2 + 3 + 5 = 10 prime numbers of books on the shelves.
• Since 24 is a composite number, we need to find the prime factors of 24, which are 2 x 2 x 2 x 3. We can package the cupcakes in boxes of 4 (2 x 2) or 6 (2 x 3). To find the number of boxes, we divide 24 by 4 or 6. 24 ÷ 4 = 6 boxes, and 24 ÷ 6 = 4 boxes.

In conclusion, mastering prime and composite numbers requires practice and patience. By working through these exercises, you’ll become more confident in your ability to identify prime and composite numbers, find prime factors, and solve real-world problems involving these concepts.