NCERT 6TH CLASS MATHEMATICS CHAPTER PLAYING WITH NUMBERS
FACTORS
Any number which is an exact divisor of a given number is called a factor of the given number.
For example factor of 6 are 1, 2, 3 and 6
Important results :
(a) 1 is a factor of every number.
(b) Every number is a factor of itself.
(c) Every factor of a number is always equal to or less than the number.
(d) Every number has a finite number of factors.
MULTIPLES
Just as 1, 2, 3 and 6 are factors 6, we say that 6 is multiple of 1, 2, 3 and 6
A number is a multiple of each of its factors
Important results :
(a) Every number is a multiple of itself.
(b) Every multiple of a number is equal to or greater than the number
(c) Every number has as infinite number of multiples.
TYPES OF NUMBERS
(a) Even Number : A number which is exactly divisible by 2 is called an even number.
(b) Odd Number : A number which is not exactly divisible by 2 is called an odd number.
Example of odd numbers are : 1, 13, 15, 25, 29, ...........
(c) Prime Numbers : A natural number greater than 1, which has no factors except 1 and itself is called a prime number.
Examples of prime numbers are : 2, 3, 5, 11, 13, 17, ........
NOTE:
Every even number greater than 4 can be expressed as a sum of two odd prime numbers,
e.g., 6 = 3 + 3; 18 = 5 + 13; 44 = 13 + 31.
(d) Composite Numbers : A number is composite if it has at least one factor other than 1 and itself.
Example of composite numbers are 4, 6, 8, 9, 10, 12, 14,........
NOTE:
1. 1 is neither prime nor composite.
2. Every natural number except 1 is, either a prime number or a composite number.
3. 2 is the only prime number which is even. All other prime numbers are odd.
(e) Twin primes : Pairs of prime numbers that have a difference of 2 are called twin primes.
Example of twin primes are : (3, 5), (5, 7), (11, 13), (17, 19),........
(f) Perfect Numbers : If the sum of all the factors of a number is twice the number, then number is called a perfect number. For example, 6 is a perfect number since the factors of 6 are 1, 2, 3, 6 and their sum 1 + 2 + 3 + 6 = 2 × 6.
(g) Coprime Number : Two numbers are said to be coprime if they do not have a common factor other than 1.
Examples of coprime numbers are : (8, 15); (5, 9); (2, 11)
NOTE
1. Two prime numbers are always coprime.
Related Links
NCERT 6TH CLASS MATHEMATICS CHAPTER FRACTION
NCERT 6TH CLASS MATHEMATICS CHAPTER INTEGERS
NCERT 6TH CLASS MATHEMATICS CHAPTER BASIC GEOMETRICAL IDEAS
NCERT 6TH CLASS MATHEMATICS CHAPTER PRACTICAL GEOMETRY
NCERT 6TH CLASS MATHEMATICS CHAPTER MENSURATION
NCERT 6TH CLASS MATHEMATICS CHAPTER WHOLE NUMBERS
NCERT 6TH CLASS MATHEMATICS CHAPTER RATIO AND PROPORTION
NCERT 6th CLASS ALL SUBJECT NOTES
NCERT 6TH CLASS MATHEMATICS CHAPTER INTRODUCTION TO ALGEBRA
NCERT 6TH CLASS MATHEMATICS CHAPTER SYMMETRY
NCERT 6TH CLASS MATHEMATICS CHAPTER KNOWING OUR NUMBERS
NCERT 6TH CLASS MATHEMATICS CHAPTER UNDERSTANDING ELEMENTARY SHAPES