NCERT Book Class 6 Maths Prime Time PDF Download

Chapter 5: Prime Time

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 'vada' 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, 15, 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 _____________________________.

5.1 Common Multiples and Common Factors

[Figure 5.1: Venn diagram showing multiples of 3, multiples of 5, and common multiples of 3 and 5, See in your textbook]

Figure it Out

1. At what number is 'idli-vada' said for the 10th time?
2. If the game is played for the numbers 1 to 90, find out:
   1. How many times would the children say 'idli' (including the times they say 'idli-vada')?
   2. How many times would the children say 'vada' (including the times they say 'idli-vada')?
   3. How many times would the children say 'idli-vada'?
3. What if the game was played till 900? How would your answers change?
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.

Teacher's Note

When finding common multiples of two numbers, list out the multiples of each number separately first, then identify which numbers appear in both lists. For the idli-vada game with 3 and 5, the common multiples are 15, 30, 45, ... - these are the numbers where you say 'idli-vada'. Understanding this pattern helps you answer 'Figure it Out' questions quickly.

Let us now play the 'idli-vada' game with different pairs of numbers:

1. 2 and 5,
2. 3 and 7,
3. 4 and 6.

We will say 'idli' for multiples of the smaller number, 'vada' for multiples of the larger number and 'idli-vada' for common multiples. Draw a figure similar to Fig. 5.1 if the game is played up to 60.

Yesterday, we played this game with two numbers. We ended up saying just 'idli' or 'idli-vada' and nobody said just 'vada'! Oh, what could those numbers be!? One of the numbers was 4.

Which of the following could be the other number: 2, 3, 5, 8, 10?

Jump Jackpot

Jumpy and Grumpy play a game.

• Grumpy places a treasure on some number. For example, he may place it on 24.
• Jumpy chooses a jump size. If he chooses 4, then he has to jump only on multiples of 4, starting at 0.
• Jumpy gets the treasure if he lands on the number where Grumpy placed it.

Which jump sizes will get Jumpy to land on 24?

If he chooses 4: Jumpy lands on 4 \( \rightarrow \) 8 \( \rightarrow \) 12 \( \rightarrow \) 16 \( \rightarrow \) 20 \( \rightarrow \) 24 \( \rightarrow \) 28 \( \rightarrow \) ...

Other successful jump sizes are 2, 3, 6, 8 and 12.

[Figure: Number line from 0 to 24 with various jumps marked showing different jump sizes, See in your textbook]

What about the jump of sizes 1 and 24? Yes, they also will land on 24.

The numbers 1, 2, 3, 4, 6, 8, 12, 24 all divide 24 exactly. Recall that such numbers are called factors or divisors of 24.

Teacher's Note

A factor of a number always divides it with no remainder. For 24, you can check each number: does 2 divide 24? Yes, \( 24 \div 2 = 12 \). Does 5 divide 24? No, \( 24 \div 5 = 4.8 \). So 5 is not a factor of 24. Use this test when the book later asks you to find all factors of a number.

Grumpy increases the level of the game. Two treasures are kept on two different numbers. Jumpy has to choose a jump size and stick to it. Jumpy gets the treasures only if he lands on both the numbers with the chosen jump size. As before, Jumpy starts at 0.

Grumpy has kept the treasures on 14 and 36. And, Jumpy chooses a jump size of 7.

Will Jumpy land on both the treasures? Starting from 0, he jumps to 7 \( \rightarrow \) 14 \( \rightarrow \) 21 \( \rightarrow \) 28 \( \rightarrow \) 35 \( \rightarrow \) 42 ... We see that he landed on 14 but

Key Points

• A multiple of a number is obtained by multiplying it by any whole number. For example, multiples of 3 are 3, 6, 9, 12, 15, ... and multiples of 5 are 5, 10, 15, 20, 25, ...
• A common multiple of two numbers is a number that appears in the multiple lists of both. For 3 and 5, the common multiples are 15, 30, 45, ... (these are multiples of both).
• A factor (or divisor) of a number is a whole number that divides it exactly with no remainder. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

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