PLAYING WITH NUMBERS (POST 2)

This is our 2nd class

Welcome to mathematics blog lesson.

In the last class we discussed about Factors and multiples.
Today we will read and discuss about Prime and composite numbers.

Topic is -"Playing with numbers"

Learning Objectives:  By the end of this lesson, you will be able to:

1. define 'Prime number' and 'Composite number'.

2. identify Prime and Composite numbers.

3. explain characteristics of prime and composite numbers.

In math, some terms often confuse the students; a good example of this is the difference between “prime numbers” and “composite numbers.” It can be quite complicated to some, but actually, it is really simple. It all relates to the concept of natural numbers and their factors .

Prime Numbers: A prime number is the one which has exactly two factors, which means, it can be divided by only the number “1” and itself. But the number “1” is not a prime number.

Example of Prime Number:

3 is a prime number because 3 can be divided by only two number’s i.e. 1 and 3 itself.

In the same way, 2, 5, 7, 11, 13, 17 are prime numbers.

Composite Numbers: A composite number has more than two factors, which means apart from getting divided by number 1 and itself, it can also be divided by at least one integer or number. We don’t consider the number ‘1’ as a composite number.

Example of Composite Number:

12 is a composite number because it can be divided by 1,2,3,4,6 and 12. So, the number ‘12’ has 6 factors.

let's watch a video:

Moreover, the Greek mathematician Eratosthenes designed a quick way to find all the prime numbers.It's a process called the Sieve of Eratosthenes.

The idea is to find numbers in the table that are multiples of a number and therefore composite. The numbers that are left will be prime numbers.

Thus, to find prime numbers between 1 and 100 with the Sieve of Eratosthenes (refer to Page no.52 of the textbook).

Important points to remember:

1. The first four Prime numbers are 2, 3, 5 and 7.Every composite number less than 100 is divisible by at least one of these numbers.This fact makes it easy to test whether a number under 100 is prime or not. Simply test it for divisibility by 2, 3 ,5 and 7.

2. The smallest composite number is 4.

3. The smallest Prime number is 2.

4. The only even prime number is 2. All other even numbers are composite numbers.

5. the number 1 is neither a prime number nor a composite number.

Now, let us Start Exercise 3.2 (Page no. 53)
Q1: (a) What is the sum of any two odd numbers?
Solution: Let us try some examples
Example 1:     3 + 7 = 10
Example 2:    5 + 13 = 18
Example 3:   11 + 23 = 34

Hence, it is proved that sum of any two odd numbers is always an even number.

Q1 (b) do it on your own.

Q2: True /False:
a) False ( For e.g- 1 + 3 + 5 = 9).
b) True (For e.g- 5 + 7 + 8 = 20).
c) True (For e.g- 7 x 5 x 3 = 105).
d) False (For e.g -34/2 = 17,  20/2 = 10)
e) False (2 is an even prime number.)
f) False (Prime numbers have 2 factors)
g) False ( for e.g- 2 + 3 = 5)
h) True ( as, except 2 all other even numbers are divisible by 2)
i) False (2 is an even prime number)
j) True (For e.g- 6 x 4 = 24)

HOMEWORK
Do Q3, 4, 5, 8 and 9 (Ex-3.2, pg.no. 53).

That's all for today.

         If you have any doubt, post it in the comment section below.

         Take care.

         GOD BLESS !!

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