Class 6 Mathematics Prime Time notes covering common multiples and factors, prime and composite numbers, co-prime numbers, prime factorisation and divisibility tests.
Prime Time is the chapter where numbers start behaving like characters in a game. You meet the 'idli-vada' game, where multiples of 3 and 5 are called out as words, and the treasure hunt game, where jump sizes decide which numbers you can land on. These games quietly teach two big ideas: common multiples and common factors. From there the chapter moves to prime and composite numbers, the Sieve of Eratosthenes for listing primes up to 100, co-prime pairs, and prime factorisation — writing every number greater than 1 as a product of primes. You also learn quick divisibility tests for 2, 5, 10, 4 and 8, so you can spot factors without long division. By the end, you will be able to break numbers into primes, check whether two numbers are co-prime, and decide divisibility using patterns instead of guesswork.
What you'll learn
1Identify common multiples and common factors of two or more numbers
2Classify numbers as prime, composite or neither, using the number of factors
3List prime numbers up to 100 using the Sieve of Eratosthenes
4Define co-prime numbers and check whether a given pair is co-prime
5Write the prime factorisation of a number and use it to test divisibility
6Apply divisibility tests for 2, 5, 10, 4 and 8 without doing long division
7Recognise special numbers such as perfect numbers and twin primes
Chapter at a glance
01Chapter Overview
02Factors and Multiples
03Prime and Composite Numbers
04Prime Factorization and HCF
05Least Common Multiple (LCM)
Detailed chapter notes
01
Common Multiples and Common Factors
In the 'idli-vada' game, players say 'idli' for multiples of 3, 'vada' for multiples of 5, and 'idli-vada' for numbers that are multiples of both. The first such number is 15. Numbers that are multiples of two or more numbers together are called common multiples. In the treasure hunt game, Jumpy starts at 0 and jumps in equal steps. If a treasure is on 24, jump sizes 1, 2, 3, 4, 6, 8, 12 and 24 all land on it — these are the factors of 24. When treasures are on 14 and 36, only jump sizes that are factors of both numbers work, that is, the common factors. So common factors are the numbers that divide two or more given numbers exactly, and common multiples are the numbers that both given numbers divide exactly.
Common multiplea number that is a multiple of each of the given numbers
Common factora number that is a factor of each of the given numbers
The first common multiple of 3 and 5 is 15
Common factors of 14 and 36 are 1 and 2
02
Prime and Composite Numbers
Guna tried to arrange 12 figs in rectangles and found several arrangements: 1 × 12, 2 × 6 and 3 × 4. Anshu could arrange 7 figs in only one way: 1 × 7. The difference is in the number of factors. Numbers like 7, which have exactly two factors — 1 and the number itself — are called prime numbers. The first few primes are 2, 3, 5, 7, 11, 13, 17 and 19. Numbers like 4, 6, 8, 9, 10 and 12 have more than two factors and are called composite numbers. The number 1 has only one factor, so it is neither prime nor composite. To list all primes up to 100, we use the Sieve of Eratosthenes: cross out 1, circle 2 and cross out its multiples, then circle 3 and cross out its multiples, and continue. The circled numbers are prime.
Prime numberhas exactly two factors, 1 and itself
Composite numberhas more than two factors
1 is neither prime nor composite
Sieve of Eratosthenesa step-by-step method to list primes
2 is the only even prime number
03
Co-prime Numbers
In the treasure game, a jump size of 1 is not allowed. Grumpy wants to place two treasures so that Jumpy cannot reach both. If the treasures are on 4 and 9, no jump size other than 1 reaches both, so the pair is safe. If they are on 12 and 26, a jump size of 2 reaches both, so the pair is not safe. Two numbers that have no common factor other than 1 are called co-prime numbers. For example, 4 and 9 are co-prime, while 15 and 39 are not, because 3 is a common factor. Any two prime numbers are always co-prime. When two numbers are co-prime, their first common multiple is simply their product.
Co-prime numbersno common factor other than 1
4 and 9 are co-prime; 15 and 39 are not
Any two prime numbers are co-prime
If two numbers are co-prime, their first common multiple is their product
04
Prime Factorisation
Every number greater than 1 can be written as a product of prime numbers. This is called its prime factorisation, and the primes used are its prime factors. For example, 56 = 2 × 2 × 2 × 7, and 36 = 2 × 2 × 3 × 3. You can split a number in many ways, but the final set of prime factors is always the same except for the order in which they are written. Usually we write the primes in increasing order. The number 1 has no prime factorisation. Prime factorisation helps us check whether two numbers are co-prime: if their prime factorisations share no common prime, the numbers are co-prime. It also helps test divisibility: one number divides another exactly when the prime factorisation of the second is included in the prime factorisation of the first.
Prime factorisationwriting a number as a product of primes
56 = 2 × 2 × 2 × 7; 36 = 2 × 2 × 3 × 3
The prime factorisation of a number is unique, apart from order
No common prime factor means the two numbers are co-prime
If the prime factorisation of one number is included in that of another, the second is divisible by the first
05
Divisibility Tests
Divisibility tests let us check factors quickly, without long division. A number is divisible by 10 if it ends in 0, by 5 if it ends in 0 or 5, and by 2 if it ends in 0, 2, 4, 6 or 8. For 4, the last digit is not enough — 12 is a multiple of 4 but 22 is not, even though both end in 2. Instead, only the last two digits matter: if the number formed by the last two digits is divisible by 4, the whole number is divisible by 4. For example, 8536 is divisible by 4 because 36 is. For 8, only the last three digits matter: if the number formed by the last three digits is divisible by 8, the whole number is divisible by 8. Tests for 3, 6, 7 and 9 are studied in later classes.
Divisible by 10ends in 0
Divisible by 5ends in 0 or 5
Divisible by 2ends in 0, 2, 4, 6 or 8
Divisible by 4last two digits form a multiple of 4
Divisible by 8last three digits form a multiple of 8
06
Special Numbers and Fun with Numbers
The chapter closes with puzzles and special kinds of numbers. A perfect number is one for which the sum of all its factors is twice the number. For example, the factors of 28 are 1, 2, 4, 7, 14 and 28, and their sum is 56, which is twice 28. The number 6 is also a perfect number. Twin primes are pairs of primes that differ by 2, such as 3 and 5, or 17 and 19. Prime puzzles ask you to fill a grid with prime numbers so that the product of each row equals the number to its right, and the product of each column equals the number below it. These activities show how prime factorisation is used as a tool for solving puzzles, not just for calculations.
Perfect numbersum of all factors equals twice the number (for example, 6 and 28)
Twin primesprimes with a difference of 2 (for example, 3 and 5, 17 and 19)
Prime puzzles use prime factorisation to fill grids
Prime numbers are the building blocks of all whole numbers
Want the complete chapter resources?Topic notes, quizzes and flashcards for Prime Time.
Q1. Define prime numbers and composite numbers. Give one example of each.
Show model answer
Model answer
Prime numbers are numbers that have only two factors: 1 and the number itself. For example, 7 is a prime number because its only factors are 1 and 7. Composite numbers are numbers that have more than two factors. For example, 8 is a composite number because its factors are 1, 2, 4, and 8.
Sample question3 marks
Q2. In the 'idli-vada' game, for which numbers do the players say 'idli-vada'? What are these numbers called? Give the first three such numbers.
Show model answer
Model answer
Players say 'idli-vada' for numbers that are multiples of both 3 and 5. These numbers are called common multiples of 3 and 5. The first three such numbers are 15, 30, and 45.
Sample question3 marks
Q3. Define prime numbers and composite numbers with examples. Also, state whether 1 is prime or composite.
Show model answer
Model answer
Prime numbers are numbers that have exactly two factors: 1 and the number itself. For example, 2, 3, 5, 7, 11 are prime numbers. Composite numbers are numbers that have more than two factors. For example, 4, 6, 8, 9, 10 are composite numbers. The number 1 has only one factor, which is 1 itself, so it is neither prime nor composite.
Sample question3 marks
Q4. State the divisibility test for 10 and check whether 8560 is divisible by 10. Give a reason.
Show model answer
Model answer
A number is divisible by 10 if its last digit is 0. Since 8560 ends with 0, it is divisible by 10. This is because multiples of 10 always end with 0.
Sample question3 marks
Q5. Find the prime factorization of 56 and 63. Using these factorizations, determine whether 56 and 63 are co-prime. Explain your reasoning.
Show model answer
Model answer
Prime factorization of 56: 56 = 2 × 2 × 2 × 7. Prime factorization of 63: 63 = 3 × 3 × 7. The common prime factor is 7. Since they share a common factor other than 1, they are not co-prime.
Want more questions with answers?Get the full practice set for this chapter.
What is the difference between prime and composite numbers?
A prime number has exactly two factors: 1 and the number itself, such as 2, 3, 5, 7 and 11. A composite number has more than two factors, such as 4, 6, 8, 9 and 10. The number 1 has only one factor, so it is neither prime nor composite.
What are co-prime numbers?
Two numbers are co-prime if they have no common factor other than 1. For example, 4 and 9 are co-prime because the only factor they share is 1. Any two prime numbers are always co-prime, and when two numbers are co-prime, their first common multiple is their product.
How do you find the prime factorisation of a number?
Keep breaking the number into factors until only prime numbers are left. For example, 56 = 4 × 14 = 2 × 2 × 2 × 7. The primes 2 and 7 are the prime factors of 56. Every number greater than 1 has a prime factorisation, and it is the same whichever way you split the number, apart from the order of the factors.
What is the divisibility test for 4 and 8?
For 4, look at the last two digits: if the number they form is divisible by 4, the whole number is divisible by 4. For example, 8536 is divisible by 4 because 36 is. For 8, look at the last three digits: if the number they form is divisible by 8, the whole number is divisible by 8.
Why is 1 neither prime nor composite?
A prime number must have exactly two factors, and a composite number must have more than two factors. The number 1 has only one factor, which is 1 itself. So it does not fit either definition and is neither prime nor composite.
What is the Sieve of Eratosthenes?
It is a method for listing prime numbers. Cross out 1, circle 2 and cross out all later multiples of 2, then circle 3 and cross out all later multiples of 3, and continue with the next uncrossed number. When you finish, the circled numbers are the primes. Eratosthenes was a Greek mathematician who lived around 2200 years ago.