## CBSE Class 6 Maths Chapter 3 Notes Playing with Numbers

### Playing with Numbers Class 6 Notes Conceptual Facts

1. A number which divides a given number exactly is called a factor of the given number.

2. Every number is a factor of itself and 1 is a factor of every number.

3. Every number is a multiple of its factors.

4. Every factor is less than or equal to its multiple.

5. Every multiple of a given number is greater than or equal to that number.

6. A natural number which is not divisible by any number except 1 or itself is called prime number.

7. 2 is the only natural number which is even as well as prime. All the prime numbers except 2 are odd.

8. 2 is the smallest prime number.

9. Numbers which are not prime are called composite numbers.

10. 1 is neither prime nor composite number.

11. Two numbers are called co-prime if they have only 1 as common factor.

12. Pairs of prime numbers differ by 2 are called twin primes.

13. The factors of a given number are Finite but it may have infinite number of multiples.

14. Rule for divisibility:

- A number is divisible by 2 if it has 0 or even digits at its units place.
- A number is divisible by 3 if the sum of its digits is also divisible by 3.
- A number with 3 or more digits is divisible by 4 if the number found by last two digits of the number is divisible by 4.
- A number is divisible by 5, if it has only 0 or 5 in its units place.
- A number is divisible by 6, if it is divisible by 2 and 3 both.
- A number with 4 or more digits is divisible by 8 if the number formed by its last 3 digits are divisible by 8.
- A number is divisible by 9 if the sum of all the digits of the number is divisible by 9.
- A number is divisible by 11 if the difference between the sum of the digits at odd places taken from the right, and the sum of all the digits at even places is either 0 or divisible by 11.

15. The HCF of two or more given numbers is called the highest common factor.

16. The LCM of two or more given numbers is called lowest common multiple.

17. HCF of co-prime numbers is 1.

18. LCM of co-prime numbers is equal to their product.

19. Product of any two numbers is equal to the product of their HCF and LCM.

20. To simplify expressions involving brackets, the four fundamental operations (-, +, x, ÷) and ‘of operations, we always use the BODMAS Rule.

21. To simplify numerical expressions, we remove parenthesis ( ), curly brackets { } and square brackets [ ], strictly in this order.