Playing with Numbers
Overview
Playing with Numbers is a fun chapter that helps Class 6 students understand how numbers relate to each other through factors and multiples. We learn about divisibility rules, prime and composite numbers, HCF (Highest Common Factor), and LCM (Lowest Common Multiple). These ideas help us solve real-life problems like dividing things equally or finding common patterns. By the end of this chapter, students can work with numbers more confidently and smartly.
Typed Notes
Factors and Multiples
A factor of a number divides it completely leaving no remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12. Every number has 1 and itself as factors. A multiple is what you get when you multiply a number by a natural number. Multiples of 4 are 4, 8, 12, 16, and so on. Important points: 1 is a factor of every number, every number is a factor of itself, and every number is a multiple of itself. Factors are always finite; multiples are infinite.
Prime and Composite Numbers
A prime number has only two factors: 1 and itself. Examples are 2, 3, 5, 7, 11, and 13. The number 2 is the only even prime number. A composite number has more than two factors. Examples are 4, 6, 8, 9, 10, and 12. The number 1 is special — it is neither prime nor composite because it has only one factor. We can find prime numbers using a method called the Sieve of Eratosthenes, where we cross out multiples of primes step by step.
HCF — Highest Common Factor
The HCF of two or more numbers is the largest number that divides all of them exactly. To find HCF, first list all factors of each number, then pick the common ones, and choose the greatest. For example, factors of 12 are 1, 2, 3, 4, 6, 12 and factors of 18 are 1, 2, 3, 6, 9, 18. Common factors are 1, 2, 3, 6. So HCF is 6. We can also use the prime factorisation method or the division method to find HCF quickly and accurately.
LCM — Lowest Common Multiple
The LCM of two or more numbers is the smallest number that is exactly divisible by all of them. To find LCM, list multiples of each number and find the smallest common one. For example, multiples of 4 are 4, 8, 12, 16, 20, 24 and multiples of 6 are 6, 12, 18, 24. The smallest common multiple is 12, so LCM is 12. We can also use prime factorisation: take each prime factor the greatest number of times it appears in any number. There is a useful relation: HCF × LCM = Product of two numbers.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01A factor of a number divides it exactly with no remainder, while a multiple is obtained by multiplying the number by 1, 2, 3, and so on.
- 02A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite.
- 03HCF (Highest Common Factor) is the greatest number that divides two or more numbers exactly.
- 04LCM (Lowest Common Multiple) is the smallest number that is a multiple of two or more numbers.
- 05Divisibility rules help us quickly check if a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, or 11 without actual division.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Find all the factors of 24.
Find the HCF of 18 and 24.
Find the LCM of 4 and 6.
The HCF of two numbers is 4 and their LCM is 36. One number is 12. Find the other number.
Check whether 348 is divisible by 4.
In this chapter we learned that factors divide a number exactly and multiples are products of a number. Prime numbers have only two factors while composite numbers have more. Divisibility rules make checking division quick and easy. HCF is the greatest common divisor of two or more numbers, and LCM is the smallest common multiple. The relationship HCF × LCM = Product of the two numbers is very useful for solving problems.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which of the following is a prime number?
Q2.What is the HCF of 12 and 16?
Q3.The LCM of 5 and 8 is:
Q4.Which number is neither prime nor composite?
Mark karo — dashboard par progress dikhega.