Assertion (A): All prime numbers are odd. Reason (R): The number 2 is an even number.

A and R both correct, R explains A

A and R both correct, R does not explain A

Assertion (A): If a number is a multiple of 10, it is also a multiple of 5. Reason (R): 10 is a multiple of 5.

A and R both correct, R explains A

A and R both correct, R does not explain A

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How many questions are in the 'PRIME TIME' quiz?

The main 'Game' mode features 40 questions covering various difficulty levels. There are also solved NCERT book questions and a monthly test.

Is this quiz aligned with the NCERT syllabus for Class 6 Maths?

Yes, this quiz is meticulously designed based on the NCERT Class 6 Maths textbook, Chapter 5: 'PRIME TIME', ensuring full syllabus coverage.

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CBSE · Class 6 · 🧮 Maths · Chapter 5

PRIME TIME

Q: What topics does this quiz cover?

This quiz covers key concepts from Chapter 5, including prime numbers, composite numbers, factors, multiples, common factors, common multiples, and the Sieve of Eratosthenes.

Prime NumbersComposite NumbersFactorsMultiplesCommon FactorsCommon Multiples

Chapter 5, 'PRIME TIME', introduces fundamental concepts in number theory. Students learn to identify prime and composite numbers, understand factors and multiples, and explore the Sieve of Eratosthenes. These concepts are crucial for building a strong foundation in mathematics, aiding in future topics like fractions, ratios, and algebraic expressions. Mastering this chapter helps students develop logical reasoning and problem-solving skills.

Multiples aur Common Multiples

Multiples aur common multiples ko samajhna bahut zaroori hai. Ye aage LCM (Least Common Multiple) aur HCF (Highest Common Factor) mein kaam aayega.

Multiples Kya Hote Hain?

Jab hum ek number ko kisi bhi counting number (1, 2, 3, ...) se multiply karte hain, toh jo result aata hai, woh us number ka multiple hota hai.
Har number ke infinitely many multiples hote hain.
Har number apna first multiple hota hai (number \( \times \) 1).
Example: 5 ke multiples hain: \(5 \times 1 = 5\), \(5 \times 2 = 10\), \(5 \times 3 = 15\), \(5 \times 4 = 20\), ... toh 5, 10, 15, 20, ... ye sab 5 ke multiples hain.

Common Multiples Kya Hote Hain?

Jab do ya do se zyada numbers ke multiples mein se jo multiples common hote hain, unhe common multiples kehte hain.
Example:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...
Yahan, 15, 30, ... ye sab 3 aur 5 ke common multiples hain.

Common Multiples Nikalne ka Method:

Dono numbers ke pehle kuch multiples likho.
Un multiples mein se jo numbers dono lists mein hain, unhe identify karo.
Yehi un numbers ke common multiples honge.

Idli-Vada Game se Connection:

'Idli' bolte hain multiples of 3 par.
'Vada' bolte hain multiples of 5 par.
'Idli-Vada' bolte hain common multiples of 3 and 5 par (jaise 15, 30, 45...).

❗Important

Smallest common multiple ko LCM (Least Common Multiple) kehte hain. Ye aage ki classes mein detail mein padhenge.

💡Tip

Common multiples nikalte time, hamesha pehle kuch multiples likho, especially jab tak pehla common multiple na mil jaaye. Phir uske multiples hi aage ke common multiples honge.

Factors aur Common Factors

Factors aur common factors ka concept bhi bahut important hai, especially HCF (Highest Common Factor) ke liye.

Factors Kya Hote Hain?

Agar ek number dusre number ko exactly divide karta hai (remainder 0 aata hai), toh pehla number dusre number ka factor ya divisor hota hai.
Har number ke finite number of factors hote hain.
1 har number ka factor hota hai.
Har number apna largest factor hota hai.
Example: 12 ke factors hain: 1, 2, 3, 4, 6, 12. Kyunki ye sab numbers 12 ko exactly divide karte hain.
\(12 \div 1 = 12\)
\(12 \div 2 = 6\)
\(12 \div 3 = 4\)
\(12 \div 4 = 3\)
\(12 \div 6 = 2\)
\(12 \div 12 = 1\)

Common Factors Kya Hote Hain?

Jab do ya do se zyada numbers ke factors mein se jo factors common hote hain, unhe common factors kehte hain.
Example:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
Yahan, 1, 2, 4 ye sab 12 aur 16 ke common factors hain.

Common Factors Nikalne ka Method:

Dono numbers ke saare factors likho.
Un factors mein se jo numbers dono lists mein hain, unhe identify karo.
Yehi un numbers ke common factors honge.

Important Points:

1 hamesha common factor hota hai har do numbers ka.
Largest common factor ko HCF (Highest Common Factor) ya GCD (Greatest Common Divisor) kehte hain. Ye bhi aage ki classes mein detail mein padhenge.

📖Definition

Factor (Divisor): Ek number jo dusre number ko bina remainder ke divide karta hai.

⭐Remember

1 is a factor of every number. Har number ka sabse chhota factor 1 hota hai aur sabse bada factor woh number khud hota hai.

Prime Numbers

Prime numbers maths ke building blocks ki tarah hain. Inhe samajhna bahut zaroori hai.

Prime Numbers Kya Hote Hain?

Wo numbers jinke exactly do factors hote hain: 1 aur woh number khud, unhe prime numbers kehte hain.
Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, ...

Key Characteristics of Prime Numbers:

Smallest Prime Number: 2. Ye eklauta even prime number hai. Baaki saare prime numbers odd hote hain.
Factors: Sirf 1 aur number itself.
Factors of 2: 1, 2
Factors of 3: 1, 3
Factors of 5: 1, 5
1 is NOT a prime number. Kyunki 1 ka sirf ek hi factor hota hai (1 khud), do nahi.

Prime Numbers ki Importance:

Ye numbers 'indivisible' hote hain (except by 1 and themselves), isliye ye multiplication ke basic elements hain.
Prime Factorization mein inka use hota hai, jahan kisi bhi composite number ko prime numbers ke product ke roop mein likha jaata hai.

📖Definition

Prime Number: Ek natural number jiske exactly do factors hote hain: 1 aur woh number khud.

❗Important

2 is the only even prime number. Yaad rakhna, baaki saare even numbers 2 se divisible hote hain, isliye unke 1, 2 aur woh number khud se zyada factors ho jaate hain.

Composite Numbers

Prime numbers ke opposite hote hain composite numbers.

Composite Numbers Kya Hote Hain?

Wo numbers jinke do se zyada factors hote hain, unhe composite numbers kehte hain.
Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ...

Key Characteristics of Composite Numbers:

Smallest Composite Number: 4.
Factors: Do se zyada factors hote hain.
Factors of 4: 1, 2, 4 (teen factors)
Factors of 6: 1, 2, 3, 6 (char factors)
Factors of 9: 1, 3, 9 (teen factors)
1 is NOT a composite number. Kyunki 1 ka sirf ek hi factor hota hai.

Numbers ka Classification:

Har natural number (1 se bada) ya toh prime hota hai ya composite hota hai.
Number 1 na toh prime hai aur na hi composite hai. Ye ek unique number hai.

📖Definition

Composite Number: Ek natural number jiske do se zyada factors hote hain.

⭐Remember

Number 1 is neither prime nor composite. Ye ek common mistake hai jo students karte hain.

Sieve of Eratosthenes

Sieve of Eratosthenes ek ancient method hai jisse hum ek given range tak ke saare prime numbers ko find kar sakte hain. Ye method Greek mathematician Eratosthenes ne develop kiya tha.

Sieve of Eratosthenes Method Steps:

List Numbers: Ek list banao numbers ki, 1 se lekar us limit tak jahan tak prime numbers chahiye (e.g., 1 se 100 tak).
Cross out 1: 1 ko cross out kar do, kyunki ye na toh prime hai aur na hi composite.
Circle 2: 2 ko circle karo (ye pehla prime number hai). Phir 2 ke saare multiples (4, 6, 8, 10, ...) ko cross out kar do. (2 ko chhod kar).
Circle 3: Next uncrossed number 3 ko circle karo. Phir 3 ke saare multiples (6, 9, 12, 15, ...) ko cross out kar do. (Jo already cross ho chuke hain, unhe dobara cross karne ki zaroorat nahi).
Circle 5: Next uncrossed number 5 ko circle karo. Phir 5 ke saare multiples (10, 15, 20, 25, ...) ko cross out kar do.
Continue: Ye process tab tak continue karo jab tak list mein saare numbers ya toh circled ho jaayen ya crossed out ho jaayen.
Result: Jo numbers circled hain, woh saare prime numbers hain us range mein.

Example: Primes up to 30

Numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
1 ko cross out.
Circle 2, cross out multiples of 2: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30.
Circle 3, cross out multiples of 3: 6 (already), 9, 12 (already), 15, 18 (already), 21, 24 (already), 27, 30 (already).
Circle 5, cross out multiples of 5: 10 (already), 15 (already), 20 (already), 25, 30 (already).
Circle 7, cross out multiples of 7: 14 (already), 21 (already), 28 (already).
Next uncrossed numbers hain 11, 13, 17, 19, 23, 29. Inhe circle kar do, inke multiples is range mein ya toh already crossed hain ya fir inke multiples is range se bahar hain.
Prime Numbers up to 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Why it works: Har composite number ka ek prime factor hota hai jo us number ke square root se chhota ya barabar hota hai. Isliye, jab hum \( \sqrt{N} \) tak ke primes ke multiples ko cross out kar dete hain, toh \(N\) tak ke saare composite numbers cross ho jaate hain aur jo bach jaate hain, woh primes hote hain.

💡Tip

Sieve of Eratosthenes method ko yaad rakhna. Kabhi-kabhi exam mein ek range tak ke prime numbers identify karne ko aa jaate hain. Step-by-step process ko follow karna.

🚧Misconception

Students aksar 1 ko prime number maan lete hain ya 2 ko cross out kar dete hain. Remember: 1 is neither prime nor composite, and 2 is the smallest and only even prime.

Easy (15)

Numbers that have only two factors, 1 and the number itself, are called what?
- Composite numbers
- Prime numbers (correct)
- Even numbers
- Odd numbers
Why: Prime numbers have exactly two factors: 1 and themselves.
What is the smallest prime number?
- 1
- 0
- 2 (correct)
- 3
Why: The smallest prime number is 2, as it is the only even prime number.
Which of the following is a composite number?
- 7
- 11
- 9 (correct)
- 13
Why: A composite number has more than two factors. 9 has factors 1, 3, and 9.
Is 1 a prime number, a composite number, or neither?
- Prime number
- Composite number
- Neither prime nor composite (correct)
- Both prime and composite
Why: The number 1 has only one factor, which is itself, so it is neither prime nor composite.
Which of these numbers is a factor of 24?
- 5
- 7
- 8 (correct)
- 9
Why: A factor divides a number exactly. 8 divides 24 exactly (24 ÷ 8 = 3).
What is the next multiple of 7 after 21?
- 24
- 28 (correct)
- 30
- 35
Why: Multiples of 7 are found by multiplying 7 by consecutive integers. 7 x 4 = 28.
The numbers 1, 2, 3, 4, 6, 8, 12, 24 are all factors of which number?
- 12
- 18
- 24 (correct)
- 36
Why: These numbers all divide 24 exactly, making them factors of 24.
Which of the following is a multiple of both 3 and 5?
- 10
- 12
- 15 (correct)
- 20
Why: A common multiple is divisible by both numbers. 15 is divisible by 3 (5 times) and 5 (3 times).
The number 2 is the only even prime number.
Why: All other even numbers are divisible by 2 and thus have more than two factors.
All odd numbers are prime numbers.
Why: For example, 9 is an odd number but is composite (factors are 1, 3, 9).
Every number has at least two factors.
Why: The number 1 has only one factor, which is 1 itself.
A number that has more than two factors is called a __________ number.
Why: Composite numbers have more than two factors.
The numbers 1, 2, 3, 4, 6, 12 are the __________ of 12.
Why: These numbers divide 12 exactly, so they are its factors.
The process of finding prime numbers by systematically eliminating multiples is known as the Sieve of __________.
Why: The Sieve of Eratosthenes is a method for finding all prime numbers up to a specified integer.
Multiples of 5 are numbers like 5, 10, 15, 20, and so on. These are numbers that can be divided by 5 with no __________.
Why: A multiple is a product of a number and an integer, meaning it's perfectly divisible.

Medium (15)

Which of the following numbers is a common factor of 12 and 18?
- 4
- 6 (correct)
- 9
- 12
Why: Factors of 12 are {1, 2, 3, 4, 6, 12}. Factors of 18 are {1, 2, 3, 6, 9, 18}. The common factor is 6.
If a number is a multiple of both 4 and 6, it must also be a multiple of which number?
- 8
- 10
- 12 (correct)
- 24
Why: The least common multiple (LCM) of 4 and 6 is 12. Any common multiple must be a multiple of their LCM.
How many prime numbers are there between 20 and 30 (exclusive)?
- 1
- 2 (correct)
- 3
- 4
Why: The prime numbers between 20 and 30 are 23 and 29.
Which pair of numbers has 1 as their only common factor?
- 6 and 9
- 10 and 15
- 7 and 10 (correct)
- 12 and 18
Why: Numbers with only 1 as a common factor are called co-prime numbers. Factors of 7 are {1, 7} and factors of 10 are {1, 2, 5, 10}. Only 1 is common.
If a number is a factor of another number, then the first number must be less than or equal to the second number.
- Always true (correct)
- Always false
- Sometimes true
- Cannot be determined
Why: A factor divides a number exactly, and it cannot be greater than the number itself.
Match the numbers with their correct classification.
Why: 2 is prime, 1 is neither, 9 and 15 are composite.
Match the numbers with their factors.
Why: Factors are numbers that divide the given number exactly.
Match the numbers with their multiples (up to the 4th multiple).
Why: Multiples are obtained by multiplying the number by consecutive integers.
What is the greatest factor of 30, other than 30 itself?
Why: List factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. The greatest factor other than 30 is 15.
What is the smallest composite number?
Why: 1 is neither, 2 and 3 are prime. 4 is the first number with more than two factors (1, 2, 4).
Arrange the steps of the Sieve of Eratosthenes to find prime numbers up to 100.
Why: The Sieve of Eratosthenes starts by eliminating 1, then multiples of 2, 3, 5, and so on.
Arrange the numbers in ascending order of their number of factors.
Why: Count factors for each: 1 (1), 7 (2), 4 (3), 6 (4).
Observe the Venn diagram showing multiples of 3 and 5. Which number should be placed in the overlapping region?
- 10
- 12
- 15 (correct)
- 18
Why: The overlapping region represents common multiples. 15 is a multiple of both 3 and 5.
In the Sieve of Eratosthenes, after circling 2 and crossing out its multiples, and then circling 3 and crossing out its multiples, what is the next number you would circle?
- 4
- 5 (correct)
- 6
- 7
Why: 4 and 6 would have been crossed out as multiples of 2. 5 is the next uncrossed number.
Consider the number line showing jumps. If a jump of size 'X' lands exactly on 24, what kind of number is 'X' in relation to 24?
- A multiple of 24
- A prime number
- A factor of 24 (correct)
- A composite number
Why: If 'X' divides 24 exactly (lands on it), then 'X' is a factor of 24.

Hard (10)

What is the sum of the first five prime numbers?
Why: The first five prime numbers are 2, 3, 5, 7, 11. Their sum is 2+3+5+7+11 = 28.
How many factors does the number 36 have?
Why: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 factors.
What is the smallest number that is a multiple of 2, 3, and 5?
Why: The smallest common multiple (LCM) of 2, 3, and 5 is their product since they are all prime: 2 x 3 x 5 = 30.
How many composite numbers are there between 1 and 10 (inclusive)?
Why: The composite numbers between 1 and 10 are 4, 6, 8, 9. There are 4 of them.
Assertion (A): All prime numbers are odd. Reason (R): The number 2 is an even number.
- A and R both correct, R explains A
- A and R both correct, R does not explain A
- A correct, R wrong
- A wrong, R correct (correct)
- Both A and R are wrong
Why: Assertion is false because 2 is a prime number and it is even. Reason is true.
Assertion (A): If a number is a multiple of 10, it is also a multiple of 5. Reason (R): 10 is a multiple of 5.
- A and R both correct, R explains A (correct)
- A and R both correct, R does not explain A
- A correct, R wrong
- A wrong, R correct
- Both A and R are wrong
Why: If a number is a multiple of 10, it can be written as 10k = (5x2)k = 5(2k), showing it's a multiple of 5. This is because 10 itself is a multiple of 5.
A game is played where players say 'idli' for multiples of 3 and 'vada' for multiples of 5. If a player says 'idli-vada', what is the smallest number they could be referring to?
- 3
- 5
- 15 (correct)
- 30
Why: 'Idli-vada' means the number is a multiple of both 3 and 5. The smallest such number is the LCM of 3 and 5, which is 15.
In the 'idli-vada' game, if the game is played for numbers 1 to 60, how many times would a player say 'idli-vada'?
- 3
- 4 (correct)
- 5
- 6
Why: 'Idli-vada' is said for multiples of 15. Multiples of 15 up to 60 are 15, 30, 45, 60. That's 4 times.
The given image shows a partially completed Sieve of Eratosthenes. Which number should be circled next to identify the next prime number?
- 7 (correct)
- 8
- 9
- 10
Why: After 2, 3, and 5, the next uncrossed number in the Sieve is 7, which is prime.
Consider the Venn diagram showing common multiples of two numbers. If the numbers in the intersection are 24, 48, 72, what could be the two original numbers?
- 3 and 4
- 6 and 8 (correct)
- 12 and 16
- 24 and 48
Why: The numbers in the intersection are common multiples. The smallest common multiple (LCM) is 24. The LCM of 6 and 8 is 24.