Prime Numbers Basic 5 Mathematics Lesson Note

Learning Objectives:

1. To identify odd and even numbers
2. To recognize prime numbers less than 100
3. To understand the concept of composite numbers including factors of numbers
4. To identify multiples of numbers and find the least common multiple (LCM)

Previous Lesson:

Multiplication and Division of Whole Numbers

Embedded Core Skills:

1. Reasoning
2. Problem solving
3. Critical thinking

Learning Materials:

1. Number charts
2. Multiplication worksheets
3. Charts/posters
4. Books or flashcards with numbers
5. Chart with prime numbers less than 100
6. Worksheets with exercises

Content:

Odd and Even Numbers:

Numbers can be categorized as odd or even. Even numbers can be divided by two with no remainder, e.g. 2,4,6,8 even with even numbers are the multiples of 2.

• Odd numbers are numbers that cannot be divided evenly by 2. Example: 1, 3, 5, 7, 9, etc.
• Odd examples give one remainder to identify them.
• The last digit of an even number may be 0, 2, 4, 6, 8 and if it terminates in these digits, it will be even. Examples: 10, 22, 34, 56, 118, etc.
• Even numbers end in 0, 2, 4, 6, 8, while odd numbers end in 1, 3, 5, 7, 9.
• We can give examples of prime numbers.

Prime Numbers:

A prime number is a natural number greater than 1 that can be divided by 1 and 2 only and by itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, etc.

Examples:

• 2 is the smallest prime number because it can only be factors 1 and 2.
• 3 is a prime number as well as one divided only by one and itself.
• 5 is a prime number because its only factors are 1 and 5.

Now let’s look at some prime numbers as examples:

How to Identify Prime Numbers less than 100:

To find prime numbers, you can start with small numbers and check if they have only two factors: 1 and themselves. A prime number can only be divided exactly by 1 and by itself.

Numbers between 1 and 100 that are prime numbers are listed below:

1. Prime factors are the prime numbers that, when multiplied together, give you a particular composite number. A prime factor only has the following factors 1 and the number itself.
2. A composite number is a number that has more than 2 factors.
3. 1 and with the number you want to factor.
4. Check the number to see how many more factors (F) and continue dividing until you get 1.
5. A factor is a number that divides evenly into another number.
6. When we do the more prime factorization and repeat this process until we original number.

For example, let’s find the prime factors of 12:

• 12 can be divided by 2: 12 ÷ 2 = 6
• 6 ÷ 2 = 3 (3 is a prime factor, so write it down)
• So 12 = 2 × 2 × 3 or 2² × 3

Here’s another example with a larger number: 48

• Start with 48
• 48 ÷ 2 = 24
• 24 ÷ 2 = 12 (2 is a prime factor, so write it down)
• 12 ÷ 2 = 6 (2 is a prime factor and 2 goes into both)
• 6 ÷ 2 = 3 (2 is a prime factor, so write it down)
• 3 ÷ 3 = 1

Finding the prime factors of a number is important in various mathematical calculations, including simplifying fractions, finding common factors, and working with exponents.

How to Calculate prime numbers of given figures:

Number: 15

• Start with 15
• Divide by 3: 15 ÷ 3 = 5
• Divide by the smallest prime 3: and 5
• So the prime factors of 15 are 3 and 5
• Write down the prime factors: 3 and 5
• So the prime factorization is 3 × 5

Number: 18

• Start with 18
• Divide by 2: 18 ÷ 2 = 9
• Divide by 3: 9 ÷ 3 = 3
• Divide by 3: 3 ÷ 3 = 1
• Write down the prime factors: 2 and 3
• So the prime factorization of 18 are 2 and 3

Number: 28

• Start with 28
• Divide by 2: 28 ÷ 2 = 14
• Divide by 2: 14 ÷ 2 = 7
• Divide by 7: 7 ÷ 7 = 1
• Write down the prime factors: 2 and 7
• So the prime factorization of 28 are 2 and 7

Number: 36

• Start with 36
• Divide by 2: 36 ÷ 2 = 18
• Divide by 2: 18 ÷ 2 = 9
• Divide by 3: 9 ÷ 3 = 3
• Divide by 3: 3 ÷ 3 = 1
• Write down the prime factors: 2 and 3
• So the prime factorization of 36 are 2 and 3

Number: 42

• Start with 42
• Divide by 2: 42 ÷ 2 = 21
• Divide by 3: 21 ÷ 3 = 7
• Divide by 7: 7 ÷ 7 = 1
• Write down the prime factors: 2, 3 and 7
• So the prime factorization of 42 are 2, 3 and 7

Number: 50

1. Start with 50
2. Divide by 2: 50 ÷ 2 = 25
3. Divide by 5: 25 ÷ 5 = 5
4. Divide by 5: 5 ÷ 5 = 1
5. Write down the prime factors: 2 and 5
6. So the prime factorization of 50 are 2 and 5

Number: 60

• Start with 60
• Divide by 2: 60 ÷ 2 = 30
• Divide by 2: 30 ÷ 2 = 15
• Divide by 3: 15 ÷ 3 = 5
• Divide by 5: 5 ÷ 5 = 1
• Write down the prime factors: 2, 3 and 5
• So the prime factorization of 60 are 2, 3 and 5

Number: 72

• Start with 72
• Divide by 2: 72 ÷ 2 = 36
• Divide by 2: 36 ÷ 2 = 18
• Divide by 2: 18 ÷ 2 = 9
• Divide by 3: 9 ÷ 3 = 3
• Divide by 3: 3 ÷ 3 = 1
• Write down the prime factors: 2 and 3
• So the prime factorization of 72 are 2 and 3

Number: 84

• Start with 84
• Divide by 2: 84 ÷ 2 = 42
• Divide by 2: 42 ÷ 2 = 21
• Divide by 3: 21 ÷ 3 = 7
• Divide by 7: 7 ÷ 7 = 1
• Write down the prime factors: 2, 3 and 7
• So the prime factorization of 84 are 2, 3 and 7

Number: 90

• Start with 90
• Divide by 2: 90 ÷ 2 = 45
• Divide by 3: 45 ÷ 3 = 15
• Divide by 3: 15 ÷ 3 = 5
• Divide by 5: 5 ÷ 5 = 1
• Write down the prime factors: 2, 3 and 5
• So the prime factorization of 90 are 2, 3 and 5

Test and Assessment:

Even Numbers:

Even numbers are whole numbers that can be evenly divided by 2 without leaving a remainder.

Examples of even numbers: 2, 4, 6, 8, 10, and so on.

Odd Numbers:

Odd numbers are whole numbers that cannot be divided by 2 evenly and always leave a remainder of 1.

Examples of odd numbers: 1, 3, 5, 7, 9, and so on.

How to identify: When a whole number ends in 0, 2, 4, 6, or 8, it is even. When a number ends in 1, 3, 5, 7, or 9, it is odd.

Evaluation:

Every even number is divisible _____, but it is Divisible by 2 whenever it is divisible or is Added.

• All odd numbers have a remainder of _____ when divided by 2: 1, and 1, 2, and 3
• All even numbers have no remainder when divided by 2: True or False: True
• The factors of a number are the numbers that divide evenly into it: True or False: True
• All even numbers are multiples of _____, so 16 18 24 94: 2
• All numbers greater than 2 that end in an even digit are _____ numbers: composite
• Is 17 a prime number? Yes because it can only be divided by 1 and 17 Three of all factors
• What is the next odd number after 17? 19 18, 19 15 to 18 17
• What are the first ten multiples of 3? 3, 6, 9, 12, 15, 18, 21, 24, 27, 30