RBSE Class 6 Maths Notes Chapter 3 Playing With Numbers

These comprehensive RBSE Class 6 Maths Notes Chapter 3 Playing With Numbers will give a brief overview of all the concepts.

RBSE Class 6 Maths Chapter 3 Notes Playing With Numbers

→ The process of expressing a given number as a product of factors is called a factorization.

→ A factor of a number is an exact divisor of that number.

→ Every number is a factor of itself and every number has atleast one factor.

→ 1 is a factor of every number.

→ Every factor of a number is less than or equal to the number.

→ Each number is a multiple of its each factor.

→ Every multiple of a number is greater than the number or equivalent to the number.

→ A number may have an infinite number of multiples but the number of factors of a given number are finite.

→ Every number is a multiple of itself.

→ The number which has only two factors (the number itself and 1) is called a prime number. For example 2, 3, 5, 7,11   etc. The number which has more than two factors is called composite number. For example 4, 6, 9, etc.

→ 2 is the smallest prime number which is also an even number. All other prime numbers are odd numbers.

→ Two numbers are said to be co-prime if they do not have a common factor other than 1. For example 15 and 16, are co-prime.

→ If a number is divisible by two co-prime numbers, then it is also divisible by their product.

→ Divisibility Rules (Observing the digital unit place):

• A number is divisible by 2, if its unit’s digit is 0,2,4, 6,8 eg., 2532, 7836 etc.
• A number is divisible by 10, if its unit’s digit is zero, e g., 350,7890 etc.
• A number is divisible by 5, if its unit’s digit is either 0 or 5. e.g., 350, 225 etc.

→ Divisibility Rules (On the basis of sum of digits):

• A number is divisible by 3, if the sum of its digits is divisible by 3, e.g., 555, 783 etc.
• A number is divisible by 9, if the sum of its digits is divisible by 9, eg., 981,7227 etc.
• A number is divisible by 6, if it is divisible by both 2 and 3, e.g., 7224,5112 etc

→ Rule of Divisibility by 4 : A number is divisible by 4, if the number formed by its digits in ten’s and unit’s places is divisible by 4, e.g., 7824, 7800 etc.

→ Rule of Divisibility by 8 : A number is divisible by 8, if the number formed by its digits in hundred’s, ten’s and unit’s places is divisible by 8, e.g., 1872, 2000 etc.

→ A number is divisible by 11, if the difference of the sum of its digits in odd places and the siim of its digits in even places (starting from unit’s place) is either 0 or a multiple of 11, e.g, 715,1122 etc.

→ If a number is divisible by another number, then it is divisible by each of the factors of that numbers.

→ If two numbers are divisible by a number, then their sum and difference is also divisible by that number.

→ The HCF of two or more numbers, is biggest among all its common factors.

→ The LCM of two or more numbers is the smallest number, which is divisible by all the given numbers.