NCERT Solutions for Class 6 Maths Chapter 5 Prime Time Ex 5.1

Exercise 5.1

IDLI VADA GAME

Children sit in a circle and play a game of numbers. One of the children starts by saying ‘1’. The second player says ‘2’, and so on. But when it is the turn of 3, 6, 9, … (multiples of 3), the player should say ‘idli’ instead of the number. When it is the turn of 5, 10, … (multiples of 5), the player should say ‘v ada’ instead of the number. When a number is both a multiple of 3 and a multiple of 5, the player should say ‘idli-vada’! If a player makes any mistake, they are out. The game continues in rounds till only one person remains. For which numbers should the players say ‘idli’ instead of saying the number? These would be 3, 6, 9, 12, 18, … and so on. For which numbers should the players say ‘vada’? These would be 5, 10, 20, … and so on. Which is the first number for which the players should say, ‘idli-vada’? It is 15, which is a multiple of 3, and also a multiple of 5. Find out other such numbers that are multiples of both 3 and 5. These numbers are called _____________________________. 

Ans: These numbers are called multiples of 15.

Any number that is a multiple of both 3 and 5 will require the player to say "idli-vada." The sequence of numbers that the players should say "idli-vada" includes 15, 30, 45, 60, and so on. These numbers can be found by multiplying 15 by whole numbers (1, 2, 3, ...).

1. At what number is ‘idli-vada’ said for the 10th time? 

Ans: We know that 'idli-vada' is said when a number is a multiple of both 3 and 5, which means we are looking for multiples of 15 (since 15 is the smallest number that is both a multiple of 3 and 5). So, the multiples of 15 are:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

The 10th multiple of 15 is 150, so the 10th time ‘idli-vada’ is said at 150.

2. If the game is played for the numbers 1 to 90, find out:

a. How many times would the children say ‘idli’ (including the times they say ‘idli-vada’)? 

b. How many times would the children say ‘vada’ (including the times they say ‘idli-vada’)? 

c. How many times would the children say ‘idli-vada’? 

Ans: If the game is played from numbers 1 to 90:

a. How many times would the children say ‘idli’ (including the times they say ‘idli-vada’)?

• The children will say ‘idli’ for multiples of 3 (like 3, 6, 9, 12, etc.).

• The multiples of 3 from 1 to 90 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90

That’s 30 multiples of 3. However, 'idli-vada' is said for multiples of 15, so we must subtract those:

• The multiples of 15 from 1 to 90 are: 15, 30, 45, 60, 75, 90 (6 numbers).

So, the number of times 'idli' is said is 30 - 6 = 24 times.

b. How many times would the children say ‘vada’ (including the times they say ‘idli-vada’)?

• The children will say ‘vada’ for multiples of 5 (like 5, 10, 15, 20, etc.).

• The multiples of 5 from 1 to 90 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90

That’s 18 multiples of 5. Again, we must subtract the multiples of 15 (where 'idli-vada' is said instead of ‘vada’):

• The multiples of 15 from 1 to 90 are: 15, 30, 45, 60, 75, 90 (6 numbers).

So, the number of times 'vada' is said is 18 - 6 = 12 times.

c. How many times would the children say ‘idli-vada’?

As mentioned earlier, 'idli-vada' is said for multiples of 15. The multiples of 15 from 1 to 90 are:

15, 30, 45, 60, 75, 90 (6 times).

3. What if the game was played till 900? How would your answers change? 

Ans: If the game was played till 900, here’s how the answers would change:

a. How many times would the children say ‘idli’?

• The multiples of 3 from 1 to 900 are: 3, 6, 9, ..., 900. There are 300 multiples of 3.

• The multiples of 15 from 1 to 900 are: 15, 30, 45, ..., 900. There are 60 multiples of 15.

So, the number of times ‘idli’ is said is 300 - 60 = 240 times.

b. How many times would the children say ‘vada’?

• The multiples of 5 from 1 to 900 are: 5, 10, 15, ..., 900. There are 180 multiples of 5.

• The multiples of 15 from 1 to 900 are: 15, 30, 45, ..., 900. There are 60 multiples of 15.

So, the number of times ‘vada’ is said is 180 - 60 = 120 times.

c. How many times would the children say ‘idli-vada’?

The multiples of 15 from 1 to 900 are: 15, 30, 45, ..., 900. So, the number of times ‘idli-vada’ is said is 60 times.

4. Is this figure somehow related to the ‘idli-vada’ game? 

Hint: Imagine playing the game till 30. Draw the figure if the game is played till 60.

Ans: If you imagine the game being played till 30, and draw a pattern, you'll see that multiples of 3 and 5 (like 15) are intersections, which represent the numbers where ‘idli-vada’ is said. This shows that the numbers where both conditions overlap are multiples of 15.

Figure it Out

1. Find all multiples of 40 that lie between 310 and 410. 

Ans:

• The multiples of 40 are: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440.

• So, the multiples of 40 between 310 and 410 are 320, 360, and 400.

2. Who am I? 

a. I am a number less than 40. One of my factors is 7. The sum of my digits is 8. 

b. I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 1 more than the other. 

Ans:

a. I am a number less than 40. One of my factors is 7. The sum of my digits is 8.

• The number is 16 (Factors of 16 include 7, and 1 + 6 = 7).

b. I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 1 more than the other.

• The number is 51 (51 has factors of 3 and 5, and 5 is one more than 1).

3. A number for which the sum of all its factors is equal to twice the number is called a perfect number. The number 28 is a perfect number. Its factors are 1, 2, 4, 7, 14 and 28. Their sum is 56 which is twice 28. Find a perfect number between 1 and 10. 

Ans: The perfect number between 1 and 10 is 6. The factors of 6 are 1, 2, 3, and 6. Their sum is 1 + 2 + 3 + 6 = 12, which is twice 6.

4. Find the common factors of: 

a. 20 and 28 

b. 35 and 50 

c. 4, 8 and 12 

d. 5, 15 and 25 

Ans: 

a. 20 and 28: Common factors are 1, 2, 4.

b. 35 and 50: Common factors are 1, 5.

c. 4, 8, and 12: Common factors are 1, 2, 4.

d. 5, 15, and 25: Common factor is 5.

5. Find any three numbers that are multiples of 25 but not multiples of 50. 

Ans: Three examples are: 25, 75, 125.

6. Anshu and his friends play the ‘idli-vada’ game with two numbers, which are both smaller than 10. The first time anybody says ‘idlivada’ is after the number 50. What could the two numbers be which are assigned ‘idli’ and ‘vada’?

Ans:

• The first ‘idli-vada’ after 50 happens when the number is 60.

• Two numbers smaller than 10 with common multiples at 60 are 5 and 6.

7. In the treasure-hunting game, Grumpy has kept treasures on 28 and 70. What jump sizes will land on both the numbers? 

Ans:

• The jump size that will land on both 28 and 70 is 14 (because 14 is a common factor of both 28 and 70).

8. In the diagram below, Guna has erased all the numbers except the common multiples. Find out what those numbers could be and fill in the missing numbers in the empty regions.

Ans:

• Without seeing the diagram, the common multiples could be numbers like 12, 24, 36, 48 if the numbers involved are multiples of 12.

9. Find the smallest number that is a multiple of all the numbers from 1 to 10, except for 7. 

Ans: The smallest number is 360 (as 360 is the least common multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10, but not 7).

10. Find the smallest number that is a multiple of all the numbers from 1 to 10.

Ans: The smallest number is 2520 (This is the least common multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10).

Benefits of NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 Prime Time

• Clear Understanding of Prime and Composite Numbers: The solutions explain the concepts of prime and composite numbers in a simple and easy-to-understand manner.

• Step-by-Step Explanations: Each problem in Exercise 5.1 is solved step-by-step, helping students learn how to approach and solve problems systematically.

• Improves Number Theory Skills: The exercise strengthens students' number theory knowledge by teaching them about divisibility rules and factorisation.

• Aligned with CBSE Syllabus: The solutions are fully aligned with the CBSE Class 6 Maths syllabus, ensuring that students cover all essential topics.

• Boosts Exam Preparation: These solutions provide ample practice, making it easier for students to revise and prepare confidently for exams.

• Free PDF Access: Students can download the NCERT Solutions in FREE PDF format, allowing for easy access and convenient study.

Class 6 Maths Chapter 5: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 5 - Prime Time

Conclusion

The NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1, Prime Time, offer a clear and structured way for students to master the concepts of prime and composite numbers. With step-by-step explanations, these solutions simplify the process of learning divisibility rules and factorisation. Aligned with the CBSE syllabus, they serve as an excellent tool for exam preparation and regular practice. Available for FREE PDF download, these solutions provide a convenient and effective way for students to strengthen their number theory skills and boost their confidence in solving mathematical problems.

Chapter-Specific NCERT Solutions for Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Maths Class 6

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.