# NCERT Class 6 Mathematics Chapter 3 Number Play: Summary, Concepts, and Revision Notes | SwaVid Chapter 3, "Number Play", introduces fundamental concepts of number theory that are crucial for building a strong mathematical foundation. It explores t... Canonical: https://swavid.com/maths/class/6/chapter/number-play Source: https://swavid.com/maths/class/6/chapter/number-play # Number Play ## Concepts in this chapter ## The ideas this chapter keeps returning to ## Where this chapter usually trips people up ## Find the gaps before this chapter finds them for you. ## Related chapters ### Factors and Multiples Chapter 3 · Class 6 Mathematics Chapter 3, "Number Play", introduces fundamental concepts of number theory that are crucial for building a strong mathematical foundation. It explores the relationships between numbers through factors, multiples, prime numbers, and composite numbers. The chapter also teaches practical divisibility rules and methods for finding the Highest Common Factor (HCF) and Lowest Common Multiple (LCM), essential skills for solving various arithmetic problems. Your study route Key topics A factor of a number is an exact divisor of that number. A multiple of a number is a number obtained by multiplying it by some natural number. For example, 2 is a factor of 6 because 6 divided by 2 leaves no remainder. 6 is a multiple of 2 because 2 multiplied by 3 equals 6. Example Factors of 12 are 1, 2, 3, 4, 6, 12. (Page 36) Multiples of 4 are 4, 8, 12, 16, 20, ... (Page 37) Watch out Students often confuse factors with multiples. They might say 12 is a factor of 3, or 3 is a multiple of 12. A factor of a number is an exact divisor of that number. A multiple of a number is a number obtained by multiplying it by some natural number. For example, 2 is a factor of 6 because 6 divided by 2 leaves no remainder. 6 is a multiple of 2 because 2 multiplied by 3 equals 6. Tap the card for an example Example Factors of 12 are 1, 2, 3, 4, 6, 12. (Page 36) Multiples of 4 are 4, 8, 12, 16, 20, ... (Page 37) Why it matters Understanding factors and multiples is fundamental for simplifying fractions, finding common denominators, and grasping concepts like HCF and LCM. It helps in basic arithmetic and problem-solving. Watch out Students often confuse factors with multiples. They might say 12 is a factor of 3, or 3 is a multiple of 12. Ask at home Ask the child to list all factors of 24 and the first five multiples of 7. Then ask them to explain the difference between a factor and a multiple using their examples. This chapter delves into the fascinating world of numbers, starting with factors and multiples, explaining how they define the divisibility of numbers. Students learn about prime numbers, which have exactly two factors, and composite numbers, which have more than two. The unique nature of the number 1 is highlighted, being neither prime nor composite. Key divisibility rules for numbers like 2, 3, 4, 5, 6, 8, 9, 10, and 11 are introduced, simplifying the process of checking divisibility without performing long division. The chapter then moves to prime factorisation, a method to express any composite number as a product of its prime factors. Finally, it covers the concepts of Highest Common Factor (HCF) and Lowest Common Multiple (LCM), providing methods to calculate them and demonstrating their application in real-world problem-solving scenarios, laying a strong groundwork for advanced number theory. Chapter summary This chapter delves into the fascinating world of numbers, starting with factors and multiples, explaining how they define the divisibility of numbers. Students learn about prime numbers, which have exactly two factors, and composite numbers, which have more than two. The unique nature of the number 1 is highlighted, being neither prime nor composite. Key divisibility rules for numbers like 2, 3, 4, 5, 6, 8, 9, 10, and 11 are introduced, simplifying the process of checking divisibility without performing long division. The chapter then moves to prime factorisation, a method to express any composite number as a product of its prime factors. Finally, it covers the concepts of Highest Common Factor (HCF) and Lowest Common Multiple (LCM), providing methods to calculate them and demonstrating their application in real-world problem-solving scenarios, laying a strong groundwork for advanced number theory. What you should learn Keep these close A factor of a number is an exact divisor of that number. A multiple of a number is obtained by multiplying it by a natural number. 1 is a factor of every number and every number is a multiple of itself. Prime numbers have exactly two factors: 1 and the number itself. Composite numbers have more than two factors. The number 1 is neither prime nor composite. Divisibility rules provide quick ways to check if a number is divisible by another. Prime factorisation expresses a number as a product of its prime factors. HCF is the greatest common factor of two or more numbers. LCM is the lowest common multiple of two or more numbers. Co-prime numbers have only 1 as their common factor. Twin primes are prime numbers that differ by 2. Common confusions It is easy to think Thinking 1 is a prime number. The clearer idea A prime number must have exactly two factors. 1 has only one factor (itself), so it is neither prime nor composite. It is easy to think Confusing factors with multiples (e.g., "10 is a factor of 5" or "5 is a multiple of 10"). The clearer idea Factors divide a number exactly (e.g., 5 is a factor of 10). Multiples are products of a number with another natural number (e.g., 10 is a multiple of 5). It is easy to think Believing all odd numbers are prime (e.g., 9 is prime). The clearer idea An odd number can be composite if it has more than two factors (e.g., 9 has factors 1, 3, 9). Only 2 is an even prime number. It is easy to think Forgetting to break down all factors into prime numbers during prime factorisation (e.g., writing 12 = 2 x 6 and stopping). The clearer idea Prime factorisation requires all factors in the final product to be prime numbers. Continue breaking down composite factors until only primes remain (e.g., 12 = 2 x 2 x 3). It is easy to think Confusing HCF and LCM, especially in word problems. The clearer idea HCF involves finding the largest common divisor (e.g., for dividing things into equal groups). LCM involves finding the smallest common multiple (e.g., for finding when events will coincide). Before you push ahead Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns. Keep exploring Class 6 Source - Define and identify factors and multiples of given numbers. - Distinguish between prime and composite numbers, and identify co-prime and twin prime numbers. - Apply divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, and 11 to determine if a number is divisible by another. - Perform prime factorisation of numbers using both factor tree and division methods. - Calculate the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two or more numbers. - Solve word problems involving factors, multiples, HCF, and LCM. - Define and identify factors and multiples of given numbers. - Distinguish between prime and composite numbers, and identify co-prime and twin prime numbers. - Apply divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, and 11 to determine if a number is divisible by another. - Perform prime factorisation of numbers using both factor tree and division methods. - Calculate the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two or more numbers. - Solve word problems involving factors, multiples, HCF, and LCM. - NCERT Class 6 Mathematics textbook: Ganita Prakash : Chapter 3: Number Play ## Key Links - [NCERT Mathematics](https://swavid.com/maths) - [Class 6](https://swavid.com/maths/class/6) - [Start with concepts](https://swavid.com/maths/class/6/chapter/number-play) - [Check a prerequisite](https://swavid.com/learning-debt-identifier) - [Concepts](https://swavid.com/maths/class/6/chapter/number-play) - [Practice](https://swavid.com/maths/class/6/chapter/number-play/practice-questions) - [NCERT Solutions](https://swavid.com/maths/class/6/chapter/number-play/ncert-solutions) - [Find the gaps before this chapter](https://swavid.com/learning-debt-identifier) - [Learn this chapter adapted to you](https://swavid.com/learning-style-test) - [Previous chapter 2 . 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