Students can go through AP 6th Class Maths Notes Chapter 3 Playing with Numbers to understand and remember the concepts easily.
Class 6 Maths Chapter 3 Notes Playing with Numbers
Divisibility Rules :
→ A number is divisible by 2 if it has any one of the digits 0, 2, 4, 6 or 8 in its ones place.
→ If the sum of the digits is a multiple of 3, then the number is divisible by 3.
→ If a number is divisible by both 2 and 3, then it is also divisible by 6.
→ A number is divisible by 9, if the sum of the digits of the number is divisible by 9.
→ A number is divisible by 5, if it has ‘0’ or 5 in its ones place.
→ A number is divisible by 10, if it has ‘0’ in its ones place.
→ A number is divisible by 4, if the number formed by its last two digits (i.e., tens and ones) is divisible by 4.
→ A number with 4 or more digits is divisible by 8, if the number formed by its last three digits is divisible by 8.
→ A given number is divisible by 11, if the difference between the sum of the digits at odd places and the sum of the digits at even places (from the right) is either ‘0’ or divisible by 11.
→ Factors : A number which divides the other number exactly is called a factor of that number. Ex : 1, 2, 3, 4, 6, 12 are the.factors of 12.
Note:
- 1 is a factor of every number and is the smallest of all factors.
- Every number is a factor of itself and is the greatest of its factors.
→ Prime and Composite numbers :
Prime numbers : The numbers whose only factors are 1 and the number itself are called Prime numbers. Ex : 2, 3, 5, 7, 11, 13 and so on.
The number 1 has only one factor (i.e., itself) so, 1 is neither prime nor composite. Composite numbers : Numbers having more than two factors are called composite numbers.
Ex : 4, 6, 8, 9 and so on.
The factors of 4 are i, 2, 4. The factors of 6 are 1, 2, 3, 6.
The factors of 8 are 1, 2, 4, 8. The factors of 9 are 1, 3, 9.
→ Co-prime numbers: Two numbers with only 1 as common factor are called co-primes or relatively prime. Ex : 2, 3; 7, 8.
→ Twin primes : Twin primes are prime numbers that differ from each other by two.
Ex : (3, 5), (5, 7), (11, 13), (17, 19), (41, 43) etc.
→ Common factors : Common factors are those numbers which are factors of all the given numbers.
Ex : The factors of 6 are 1, 2, 3, 6.
The factors of 12 are 1, 2, 3, 4, 6, 12.
∴ The commort factors of 6 and 12 are 1, 2, 3, 6.
→ Highest Common Factor (HCF) : The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also called the Greatest Common Divisor (GCD).
→ Least Common Multiple (LCM) : The Least Common Multiple of two or more given numbers is the lowest (or smallest or least) of their common multiples.
→ Relationship between LCM and HCF: Product of LCM and HCF = Product of the two numbers.