Chapter 3 Playing with Numbers Class 6 Notes Maths
Chapter 3 Playing with Numbers Class 6 Notes Maths is given on this page which will helpful in easily memorize formulas so you will be very confident about your understanding by now. You will understand the various factors through which one can improve their efficiency and eventually scores higher in the exam. Also, NCERT Solutions for Class 6 Chapter 3 Maths that will be useful in the preparation of exams. These Revision notes for Class 6 will be make sure that a student has understood the specifics of every topics in clear and precise manner. It will make entire memorizing process effortless and entertaining.
Factors
• A factor of a number is an exact divisor of that number.
• 1 is a factor of every number.
• Every number is a factor of itself.
• Every factor is less than or equal to the given number.
• Number of factors of a given number are finite.
Multiples
• A number is said to be a multiple of any of its factors.
• Every multiple of a number is greater than or equal to that number.
• The number of multiples of a given number is infinite.
• Every number is a multiple of itself.
Prime Numbers
• Prime numbers: Each of the numbers which have exactly two factors namely, 1 and the number itself, are called prime numbers, For example, 2, 3, 5, 7, 11, .... etc. 2 is the smallest prime number which is even. Every prime number except 2 is odd.
• Twin prime : Two consecutive odd prime numbers are known as twin prime. For example, 3 and 5.
• Prime triplet : A set of three consecutive prime numbers, differing by 2, is called a prime triplet. The only prime triplet is (3, 5, 7).
• Co-primes : Two numbers are said to be co-prime if they do not have a common factor other than 1. For example, 2 and 3. Any two prime numbers are always co-prime but converse is not always true.
• Composite numbers : The numbers having more than two factors are known as composite numbers.
For example, 4, 6, 8, 9, 10, 12, 14, .... etc. and 1 is neither prime nor composite because it has a single factor.
• Even number : All multiples of 2 are called even number.
• Odd number : Numbers which are not multiples of 2 are called odd numbers.
Divisibility Test
• A number is divisible by 2, if its unit digit are 0, 2, 4, 6 or 8.
• A number is divisible by 3, if the sum of its digits is divisible by 3.
• A number is divisible by 4, if the number formed by last two digits is divisible by 4.
• A number is divisible by 5, if its unit digit is 0 or 5.
• A number is divisible by 6, if the number is divisible by 2 and 3.
• A number is divisible by 8, if the number formed by last three digits is divisible by 8.
• A number is divisible by 9, if the sum of its digits is divisible by 9.
• A number is divisible by 11, if the difference of the sum of its digits in odd places and the sum of its digits in even places is either 0 or a multiple of 11.
Common Factors and Common Multiples
• The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common Divisor (GCD).
• The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples.
• HCF × LCM = Product of the numbers. This property is valid for two numbers only.
Some More Divisibility Rules
• If a number is divisible by another number then it is divisible by each of the factors of that number.
• If a number is divisible by two co-prime numbers then it is divisible by their product also.
• If two given numbers are divisible by a number, then their sum is also divisible by that number.
• If two given numbers are divisible by a number, then their difference is also divisible by that number.