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TitleNumber system--concepts and solving techniques
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Number system.

Numbers: we have ten digits , namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

A number is denoted by a group of digits called numerals.

Face value &place value of a digit in a numeral:

1. The face value of a digit in a numeral is its own value, at whatever place it may be.

For example, in the numeral 9368, the face value of 8 is 8, the face value of 6 is 6, the face value of 3 is 3, the face value of 9 is 9.

2. In a given numeral:

The place value of unit digit: (unit digit)*1.

The place value of tens digit: (tens digit)*10.

The place value of hundred’s digit: (hundred’s digit)*100.

So on….

For example, in the numeral 9368:

The place value of 8 = 8*1 =8

The place value of 3 =3*10 =30

The place value of 6 = 6*100 = 600

The place value of 9 =9*1000 =9000

Types of numbers:

1. Natural numbers: the counting numbers are called natural numbers.

Therefore 1, 2, 3, 4, 5, 6, 7 … are all natural numbers.

2. Whole numbers: all counting numbers starting from 0 are called the whole numbers.

Therefore 0, 1, 2, 3, 4, 5, 6, 7 … are all whole numbers.

Every natural number is a whole number but not every whole number is natural number. 0 is a whole number but not a natural number.

3. Integers: all counting numbers, zeros and negatives of counting numbers from the set of integers.

Therefore, ….,-5,-4,-3,-2,-1,0,1,2,3,4,5,… are all integers.

4. Even numbers: a counting number divisible by 2 is called an even number.

Therefore 0, 2, 4, 6, 8, 10, 12, 14, …etc. are all even numbers.

5. Odd numbers: a counting number not divisible by 2 are called odd numbers.

Therefore 1, 3, 5, 7,9 ,11, 13, 15, ….etc. are all odd numbers.

6. Prime numbers: a counting number, which have only two factors, namely the number itself and 1 is called prime number.

For example… 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, etc…

A Test for a number to be prime: Let x be the given number and let n be smallest counting number such that n2=x. if x is divisible by the prime number less than or equal to n then x is not a prime number, else x is prime.

For example: let us check whether 123 is prime or not.

We know that (12)2>123.

Prime numbers less than 12 are 2, 3, 5, 7, and 11

Clearly out of the above prime numbers, 3 divide 123.

Thus 123 is not a prime number.

7. Composite numbers: The natural numbers which are not prime, are called composite numbers.

Composite numbers can also be defined as the numbers which have more than two factors.

8. Co-prime numbers: Two natural numbers x and y are said to be co-prime if their HCF is 1.

For example: (2,3), (4, 5), (6, 7),(11,13) etc. are pairs of co-primes.

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