Page 38 - Maths Class 06

SO LU TION : (a) 4 and 6
Multiples of 4 are 4, 8, 12 , 16, 20, 24 , 28, 32, 36 ,...
Multiples of 6 are 6, 12 , 18, 24 , 30, 36 ,...

First three common multiples of 4 and 6 are 12, 24 and 36.
(b) 12 and 18
Multiples of 12 are 12, 24, 36 , 48, 60, 72 , 84, 96, 108 ,...

Multiples of 18 are 18, 36 , 54, 72 , 90, 108 ,…
First three common multiples of 12 and 18 are 36, 72 and 108.

Numbers and Various Types of Numbers

Numbers are the most important tools in our daily life. We use them in various activities in different ways.
For ex am ple, To know the num ber of stu dents in a par tic u lar class, to tell time, to keep a re cord, to pay
bills, to count money, etc. Num bers are end less as ev ery num ber is fol lowed by the next num ber greater
than it by one.

Even Numbers
A number which is exactly divisible by 2 is called an even number.

For ex am ple, 2, 4, 6, 8, 10, 12, ........., etc. are all even num bers. NOTE

Odd Numbers
A number is either even
A number which is not exactly divisible by 2 is called an odd num ber. or odd but it can not be
both even well as odd.
For ex am ple, 1, 3, 5, 7, 9, 11, 13, 15, ......., etc. are all odd num bers.
Prime Numbers
NOTE
The numbers other than 1 whose only factors are 1 and the number itself
are called prime num bers. The smallest prime number
is 2. 2 is the only even
For ex am ple, 2, 3, 5, 7, 11, ..., etc. are all prime num bers. number which is prime.
Composite Numbers

Numbers having more than two factors are called com pos ite num bers. NOTE
These num bers have at least one fac tor other than 1 and the num ber it self. 1 is neither a prime nor a
Since 4 has more than two fac tors, i e. . 1, 2 and 4, there fore it is a com pos ite composite number.
num ber. Sim i larly, 6, 8, 9, 10 ...., are also com pos ite num bers.

Twin Primes

If the difference between any two prime numbers is 2, then such pairs of prime numbers are called twin
primes. Examples of twin primes are (3, 5), (5, 7), (11, 13), etc.
Perfect Numbers

If the sum of all the factors of a number is twice the number, the number is called a perfect number.
For ex am ple, 6 is a per fect num ber.
Factors of 6 are 1, 2, 3 and 6.
Sum of the factors = 1 + 2 + 3 + 6 = 12.
Twice times of 6 = 2 × 6 = 12.

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