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Unit: Number System
Chapter: Classification of Numbers
Reference: – Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers, Prime & Composite Numbers, Even & Odd Numbers, Relationship Between Number Sets
After studying this chapter, you should be able to understand:
- Natural Numbers (Counting Numbers)
- Whole Numbers & Their Relationship with Natural Numbers
- Integers & Their Subsets
- Rational Numbers & Their Decimal Forms
- Irrational Numbers & Their Identification
- Real Numbers as the Union of Rational and Irrational Numbers
- Prime, Composite, Even & Odd Numbers
- Venn Diagram of Number Sets
Classification of Numbers
- Perfect Number- A number, whose sum of all its factors is twice the number is called a perfect number.
Example- Factors of 6 = 1, 2, 3, 6
Sum of its Factors = 1 + 2 + 3 + 6 = 12 = 2 × 6
So, 6 is a perfect number.
- Prime and Composite Numbers-
- The numbers (other than 1) which are divisible only by 1 and the number itself are prime numbers. They are the building blocks of all counting numbers. A prime number has only 2 factors, i.e., 1 and the number itself.
Example- 13 is a prime number
Factors of 13 = 1 and 13
Did you know?
A Strange Prime Number: 73,939,133
If we keep removing a digit from the right-hand end of the number, each of the remaining number is also prime. It is the largest number known with this property.
Can you find other such prime numbers?
- The numbers which has more than 2 factors are called composite numbers. We can get any composite number by multiplying a set of prime numbers.
Example- 12 is a composite number.
Factors of 12 = 1, 2, 3, 4, 6 and 12
Also, 12 = 2 × 2 × 3
- Any pair of prime numbers with a difference of 2 are called twin-primes.
Example- 3 and 5, 5 and 7, 11 and 13.
- Two numbers whose only common factor is 1 are called co-primes.
Example- 6 and 7, 9 and 11, 14 and 27
- Odd and Even Numbers-
- All the counting numbers which are divisible by 2 are called even numbers.
Examples- 2, 4, 6, 8, 10, ..
- All the counting numbers which are not divisible by 2 are called odd numbers.
Examples- 1, 3, 5, 7, 9, 11, ..
Do Remember
- 1 is neither prime nor a composite number.
- 2 is the only even prime number. It is also the smallest prime number.
- Any two consecutive numbers are co-primes.
