PRIME NUMBERS

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A prime number has exactly 2 factors, 1 and itself. A composite number has more than two factors. See the illustration below

1 = (1 x 1)

2 = (2 x 1)

3 = (3 x 1)

4 = (4 x 1),  (2 x 2)

5 = (5 x 1)

6 = (6 x 1), (2 x 3)

7 = (7 x 1)

8 = (8 x 1), (4 x 2)

9 = (9 x 1), (3 x 3)

10 = (10 x 1), (2 x 5)

 

In the above illustration it is easy to see that number 2, 3, 5 and 7 have only two factors, (1 and the number itself). So, they are prime numbers. While number 4, 6, 8, 9 and 10 are composite numbers because they have more than two factors.

Note that: number 1 is neither a prime nor a composite number since it has only one factor, 1.

 

 

PRIME FACTORS

Any composite number can be written as a product of prime factors.  Prime factors are all the prime numbers written in product form.

Example 1: Express 30 as a product of their prime factors.

Solution

Example 2 : Express 80 as a product of their prime factors.

Solution

Example 3 : Express 75 as a product of their prime factors.

Solution

 

MULTIPLES OF NUMBER

Example 4 :

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21 etc.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32 etc.

Multiples of 7 are 7, 14, 21, 28, 35, 42 etc.

Multiples of 10 are 10, 20, 30, 40, 50, 60 etc.

Multiples of 12 are 12, 24, 36, 48, 60, 72 etc.

 

EXERCISE

Express each of the following as a product of its prime number

1)  8                            (2)  45            (3)  28            (4)  44

5)  56                          (6)  60            (7)  54            (8)  55

9)  49                          (10)  81                      (11) 99                       (12) 100

13) Which of the following does not come after a prime number: 6, 9, 12, 14, 18?

14)  List all the odd numbers between 10 and 20.

15) What is the product of the smallest prime numbers which are greater than 2?

16) List all the prime numbers between 30 and 40.

17) Find the sum of all the even numbers between 20 and 30.

18) A prime number is a factor of 15 and 18. What is the prime number?

 

LOWEST COMMON MULTIPLES(L.C.M) AND HIGHEST COMMON FACTOR (H.C.F)

LOWEST COMMON MULTIPLE (L.C.M)

This means the smallest possible number that can be divided by a particular set of numbers

e.g. 1:   Find the l.c.m of 4, 6 and 8

Set of numbers are 4,  6 and 8

 

e.g. 2: Find the LCM of 15, 18 and 24

2×2×2×2×3×3×5=360

LCM= 360

 

e.g. 3: Find the LCM of 7, 14 and 21

 

 

e.g 4: Find the lcm of 24, 36, and 48

 

 

Exercise:

1. Find the LCM of
2. 8 and 16
3. 9 and 15

• 24 and 36

1. 21 and 28
2. 15 and 25

 

 

1. find the LCM of the following
2. 9, 15 and 45
3. 24,36 and 48

• 21,28 and 7

1. 15, 25 and 30

8, 16 and 24

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