Page 18 - SM inner class 6.cdr

+ 4 % 1 ¼ 3 ÷ ¾

×
Chapter3 6 ½ –

HCF & LCM

Finding factors and multiples of numbers help Multiples
solve many mathematical problems. It is also
The products we get when a number is
very useful when working with fractions.
multiplied by an integer (1, 2, 3, ..) are called
Factors the multiples of the given number.
The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16,
We know that if a number is divided by
18 , 20, …
another number and the remainder is "0" then
the 1st number is said to be divisible by the The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, …
2nd number. For example, The multiples of 9 are 9, 18, 27, …
Thus, a number is said to be a multiple of each
18 9 of its factors. It can also be noticed that the
1)18 2)18
–18 –18 multiple of a number is either greater than or
0 0 equal to the number itself.
Example 2. Write the first 4 multiples of 8.
Solution. First four multiples of 8 are:- 8x1,
6 3 8x2, 8x3, and 8x4.
3)18 6)18 Therefore, the first four multiple of 8 are 8,
–18 –18
0 0 16, 24, and 32.
Types of Natural Numbers

Natural numbers are classified in two ways,
2 1 either even and odd or prime and composite.
9)18 18)18
–18 –18 Even Numbers
0 0
The numbers which are divisible by 2 are

From the above it can be seen that the number called even numbers. We can also say that all
18 is divisible by 1, 2, 3, 6, 9 and 18. These multiples of 2 are even numbers. It means 2, 4,
numbers are known as the factors of the 6, 8,... are all even numbers because all
number 18, i.e, the factors of 18 are 1,2,3,6,9 numbers are multiple of 2.
and 18.
Odd Numbers
Example 1. Write all the possible factors of 24.
The numbers which are not divisible by 2 are
Solution. 24 = 2 × 12
called odd numbers. It can also be said that the
=3 × 8 numbers which are not multiples of 2 are odd
=4 × 6 numbers, i.e. 1, 3, 5, 7.... are all odd numbers.
=6 × 4
Prime Number
=8 × 3
A number having exactly two factors, 1 and the
=12 × 2
number itself, is called the prime number, i.e.
Therefore, all the factors of 24 are 1, 2, 3, 4, 2, 3, 5, 7, 11, 13, 17, 19 … are all prime
6, 8, 12, and 24.
numbers.
18
Mathematics In Focus - 6