Prime Numbers
Lesson Objectives
- Identify prime numbers less than 100.
- Express numbers as products of prime factors.
- Express prime factorization in index (exponential) form.
- Strengthen factorization and divisibility skills.
Lesson Introduction
Have you ever tried to build a tower using only special blocks that cannot be broken further? In Mathematics, prime numbers are like those special blocks. They are the "building blocks" of all whole numbers. Understanding prime numbers helps you factor numbers easily and solve larger math problems quickly.
Core Lesson Content
Definition of Prime Numbers:
A prime number is a number greater than 1 that has no other divisors except 1 and itself. Examples include 2, 3, 5, 7, 11, 13 etc.
Identifying Prime Numbers less than 100:
Here are all prime numbers less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Expressing Numbers as Products of Prime Factors:
Prime factorization means writing a number as a product of prime numbers. Example: 12 = 2 \times 2 \times 3
Expressing in Index Form:
Instead of repeating numbers, we use powers. Example: 12 = 2^2 \times 3
Worked Examples
Example 1: Is 29 a prime number?
Answer: 29 has only two factors: 1 and 29. Therefore, 29 is a prime number.
Example 2: Is 51 a prime number?
Answer: 51 is divisible by 3 (since 5 + 1 = 6 and 6 is divisible by 3). Hence, 51 is not a prime number.
Example 3: Express 30 as a product of its prime factors.
Answer: 30 = 2 \times 3 \times 5
Example 4: Express 60 as a product of prime factors in index form.
Answer: 60 = 2^2 \times 3 \times 5
Example 5: Express 84 as a product of prime factors in index form.
Answer: 84 = 2^2 \times 3 \times 7
Example 6: Find the prime factors of 45.
Answer: 45 = 3^2 \times 5
Example 7: Find the prime factorization of 72.
Answer: 72 = 2^3 \times 3^2
Example 8: Express 98 as a product of its prime factors.
Answer: 98 = 2 \times 7^2
Example 9: Find the prime factorization of 100.
Answer: 100 = 2^2 \times 5^2
Example 10: Is 97 a prime number?
Answer: 97 is only divisible by 1 and 97. Hence, it is a prime number.
Exercises
- List all prime numbers between 50 and 100.
- Determine whether 87 is a prime number.
- Express 90 as a product of prime factors in index form.
- [WAEC] Express 150 as a product of prime factors. (Past Question)
- Express 120 as a product of prime factors.
- Find the prime factorization of 135.
- [NECO] List the prime numbers between 20 and 40. (Past Question)
- Is 91 a prime number? Justify your answer.
- [JAMB] Express 81 as a product of prime factors. (Past Question)
- [NABTEC] Find the prime factorization of 196. (Past Question)
Conclusion/Recap
Today, you learned how to identify prime numbers and express any whole number as a product of prime numbers. You also practiced using index form to simplify long factorizations. Next lesson, we will explore Highest Common Factors (HCF) and Lowest Common Multiples (LCM) using prime factorization!
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