Chapter 3 playing with numbers . This ppt is only for education purpose only.

1. CHAPTER -3
PLAYING WITH NUMBERS
Factors – The divisor of a number are the factors of that
number.
The numbers 1, 2 and 4 are exact divisors of 4.
These numbers are called factors of 4.
(a) A factor of a number is an exact divisor of that number.
(b) 1 is a factor of every number.
(c) every number is a factor of itself.
(d) every factor of a number is an exact divisor of that number.
(e) every factor is less than or equal to the given number.
(f) number of factors of a given number are finite.
(g) A number for which sum of all its factors is equal to twice the
number is called a perfect number. Ex. 6, 28 etc.

2. CHAPTER -3
PLAYING WITH NUMBERS
MULTIPLES – The multiple of a number is the multiplication of
numbers.
Multiple of 5 = 5 x 1 =5, 5 x2 =10 , 5 x 3 = 15 i.e 5, 10, 15, 20
…..
(a) every multiple of a number is greater than or equal to that
number.1 is a factor of every number.
(b) The number of multiples of a given number is infinite.
(c) every number is a multiple of itself.

3. CHAPTER -3
PLAYING WITH NUMBERS
PRIME AND COMPOSITE NUMBERS
Prime Number - The numbers other than 1 whose only
factors are 1 and the number itself are called Prime numbers.
There are numbers, having exactly two factors 1 and the
number itself. Such number are 2, 3, 5, 7, 11 etc. These numbers
are prime numbers.
(a) 2 is the smallest prime number which is even.
(b) every prime number except 2 is odd.
Composite numbers - Numbers having more than two
factors are
called Composite numbers.
There are numbers having more than two factors like 4, 6, 8, 9, 10

4. CHAPTER -3
PLAYING WITH NUMBERS
PRIME AND COMPOSITE NUMBERS

5. CHAPTER -3
PLAYING WITH NUMBERS
ODD and EVEN
Even numbers Numbers – The Numbers which are
multiple of 2 are even Numbers.
the numbers 2, 4, 6, 8, 10, 12, 14, ...? You will find that each of
them is a multiple of 2. These are called even numbers.
ODD Numbers - The Numbers which are not multiple of 2 are
even Numbers.
The numbers 1, 3, 5, 7, 9, 11,...are called odd numbers. Because
they are not multiple of 2.

6. CHAPTER -3
PLAYING WITH NUMBERS
Divisibility by 10 : If a number has 0 in the ones place then it is
divisible by 10.
Divisibility by 5 : A number which has either 0 or 5 in its ones place is
divisible by 5.
Divisibility by 2 : a number is divisible by 2 if it has any of the digits
0, 2, 4, 6 or 8 in its ones place.
Divisibility by 3 : if the sum of the digits is a multiple of 3, then the
number
is divisible by 3.
Divisibility by 6 : if a number is divisible by 2 and 3 both then it is
divisible by 6.
Divisibility by 4 : a number with 3 or more digits is divisible by 4 if
the number formed by its last two digits (i.e. ones and tens) is

7. CHAPTER -3
PLAYING WITH NUMBERS
Divisibility by 11 : find the difference between the sum of the digits
at odd places (from the right) and the sum of the digits at even
places (from the right) of the number.If the difference is either 0 or
divisible by 11, then the number is divisible by 11.

8. CHAPTER -3
PLAYING WITH NUMBERS
Common Factors and Common Multiples
Common factors : common factors of 4, 12 and 16?
Factors of 4 are 1, 2 and 4.
Factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 16 are 1, 2, 4, 8 and 16.
Clearly, 1, 2 and 4 are the common factors of 4, 12, and 16.
Two numbers having only 1 as a common factor are called co-
prime
Numbers. Ex- 4 and 15 are co-prime numbers. 7 and 15, 12 and
49, 18 and 23 co-prime numbers.
Common Multiples : common multiples of 3, 5 and 6?
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, ...

9. CHAPTER -3
PLAYING WITH NUMBERS
Prime Factorisation : When a number is expressed as a product
of its factors we say that the number has been factorised.
Factorisation having only factors 2 , 3, 5, 7 which are prime
numbers. Such a factorisation of a number is called a prime
factorization.
Ex – Find prime factorisation of 980.
Ans- The prime factorisation of 980
is 2 × 2 × 5 × 7 × 7.

10. CHAPTER -3
PLAYING WITH NUMBERS
Highest Common Factor : The Highest Common Factor (HCF) of two or
more given
numbers is the highest (or greatest) of their common factors. It is also known
as Greatest Common
Divisor (GCD).

11. CHAPTER -3
PLAYING WITH NUMBERS
Lowest Common Multiple : The Lowest Common Multiple (LCM)
of two or more given numbers is the lowest (or smallest or least) of
their common multiples.
Ex - LCM of 24 and 90.
Solution : The prime factorisations of
24 and 90 are:
24 = 2 × 2 × 2 × 3; 90 = 2 × 3 × 3 × 5
In these prime factorisations the maximum
number of times the prime factor
2 occurs is three; this happens for 24. Similarly,
the maximum number of times
the prime factor 3 occurs is two; this happens
for 90. The prime factor 5 occurs
only once in 90.