# NCERT Solutions for Class 5 Maths Chapter 6 - Be My Multiple, I’ll Be Your Factor

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NCERT Solutions for Class 5 Maths

Chapter 6: Be My Multiple, I’ll Be Your Factor

The Mouse and the Cat

NCERT Page No. 87

(a) The steps on which the mouse jumps –  ____________________

(b) The steps on which the cat jumps –______________________

(c) The steps on which both the cat and the mouse jump –

(d) Can the mouse get away? Find out

If the cat starts from the 5th step and jumps five steps at a time and the mouse starts from the 8th step and jumps four steps at a time, can the mouse get away?

Answer.

(a) The steps on which the mouse jumps – 16, 18, 20, 22, 24, 26, 28

(b) The steps on which the cat jumps –  6, 9, 12, 15, 18, 21, 24, 27

(c) The steps on which both the cat and the mouse jump –  18 and 24

(d) Yes, the mouse can get away.

Cat starts from 5th step, and jumps 5 steps at a time.

So, the cat will jump the following steps:

10, 15, 20 and 25

Mouse starts from 8th step, and jumps 4 steps at a time.

So, the mouse will jump the following steps:

12, 16, 20 and 24

As we can see that both of them reach the step 20 after four jumps hence the mouse cannot get away.

NCERT Page No. 88

Who is Monto Waiting for?

1. Monto cat is waiting for somebody. Do you know for whom he is waiting? There is a trick to find out. (i) Mark with a red dot all the numbers which can be divided by 2.

(ii) Mark a yellow dot on the numbers which can be divided by 3 and a blue dot on the numbers which can be divided by 4.

(iii) Which are the boxes which have dots of all three colours?

(iv) What are the letters on top of those boxes?

(v) Write those letters below in order. Answer.

(i) and (ii): (iii) Boxes 12, 24, 36, 48 and 60 have dots of all the 3 colours.

(iv) Letters on top of those boxes are M, O, U, S and E.

(v) Letters in order are written as E, M, O, S and U.

NCERT Page No. 89

Meow Game

1. To play this game, everyone stands in a circle. One player calls out ‘one’. The next player says ‘two’ and so on. A player who has to call out 3 or a number which can be divided by 3 has to say ‘Meow’ instead of the number. One who forgets to say ‘Meow’ is out of the game. The last player left is the winner. Which numbers did you replace with ‘Meow’? 3, 6, 9…………………………

Answer.

The numbers replaced by word “Meow” are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 and so on.

2. We say these numbers are the multiples of 3. Play the game by changing the number to 4.

(i) Now, which numbers did you replace with ‘Meow’? These numbers are the multiples of 4.

(ii) Write any ten multiples of 5.

Answer.

(i) Numbers that get replaced with “Meow” are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 and so on.

(ii) Ten multiples of 5 are:

5, 10, 15, 20, 25, 30, 35, 40, 45 and 50.

NCERT Page No. 90

Dice Game

Throw two dice together. What are the numbers that turn up on the faces of the dice? Make a two-digit number using them. If it is a multiple of any of the numbers written next to the circles, you can write it in that circle. Then it is your friend’s turn. The one who can write more numbers in 10 rounds is the winner.

Hint: I have 3 and 2 on my dice. If I make 23, it is not the multiple of any of the numbers. So I will make 32, which is a multiple of 4, and write it in the red circle. Answer.

A dice has six faces with numbers 1, 2, 3, 4, 5 and 6.

Using all these numbers taking two at a time we can form the multiples of 6, 4, 5 and 7 as follows:

Multiples of 6: 12, 24, 36, 42

Multiples of 4: 12, 16, 24, 32

Multiples of 5: 15, 25, 35, 45

Multiples of 7: 14, 21, 35, 42

NCERT Page No. 91

Common Multiples

1. Think of a number. If it is a multiple of 3 write it in the red circle. If it is a multiple of 5 write it in the blue circle. Answer.

Multiples of 3 and 5 are written as: This answer is for reference only. Students may write any numbers of their choice that fit into the required conditions of questions.

2. Some numbers are multiples of both 3 and 5. So we can say that they are common to both 3 and 5. Think! If you write the multiples common to 3 and 5 in the purple part, then will they still be in both the red and the blue circles?

Which is the smallest among these common multiples? _________

Repeat the game using the numbers 2 and 7.

Write the common multiples of 2 and 7.

Answer.

Yes, the common multiples of 3 and 5 in the purple part will still be in the red and blue circles.

15 is the smallest among the common multiples.

Common multiples of 2 and 7 are: 14, 28, 42, 56, 70 and so on.

3. Repeat the game by putting the multiples of 4, 6 and 5 in the circles. (i) What common multiples of 5 and 6 did you write in the green part?

(ii) What common multiples of 4 and 6 are written in the orange part?

(iii) In which coloured part did you write the common multiples of 4, 6 and 5?

(iv) What is the smallest common multiple of 4, 6 and 5? ________

Answer.

Multiples of 4, 6 and 5 can be written in the circles as shown below: (i) Common multiples of 5 and 6 in green part: 30 and 60

(ii) Common multiples of 4 and 6 in orange part: 12, 24 and 36

(iii) Common multiples of 4, 5 and 6 is 60 which is written in grey part.

(iv) Smallest common multiple of 4, 5 and 6 is 60.

Puzzle

Tamarind Seeds

1. Sunita took some tamarind (imli) seeds. She made groups of five with them, and found that one seed was left over. She tried making groups of six and groups of four. Each time one seed was left over. What is the smallest number of seeds that Sunita had?

Answer.

ON making 4, 5 and 6 one seed is left behind each time.

So, to find the smallest number of seeds that Sunita had, we will first calculate the LCM of 4, 5 and 6 and then add 1 to it.

LCM of (4, 5, 6) = 60 Adding 1 to it, we get 61.

Hence, the smallest number of seeds which Sunita has is 60 +1 = 61

NCERT Page No. 93

2. Ammini is arranging 12 tamarind seeds in the form of different rectangles. Try to make more rectangles like this using 12 tamarind seeds. How many different rectangles can you make?

Answer.

With 12 tamarind seeds, we have rectangles of sizes:  12 x 1, 4 x 3 and 6 x 2. Thus, three rectangles can be made using 12 seeds. 3. If there are 15 tamarind seeds how many rectangles can you make?

Answer.

If there are 15 tamarind seeds then we have rectangles of sizes: 1 x 15, 3 x 5. So, we can make two rectangles from 15 tamarind seeds as shown below: 4. Colouring the Grid In the grid here, a rectangle made of 20 boxes is drawn. The width of this rectangle is 2 boxes.

(i) What is its length?

(ii) Colour a rectangle made of 20 boxes in some other way.

(iii) What is the length and width of the rectangle you coloured?

(iv) In how many ways can you colour a rectangle of 20 boxes? Colour them all in the grid, and write the length and width of each rectangle you have coloured.

Answer.

(i) Length of the rectangle is 10 boxes.

(ii) Rectangles made of 20 boxes in different ways are shown below: (iii) Rectangles of following length and width can be made: 5 x 4, 10 x 2, 20 x 1

(iv) This can be done in three ways: 10 x 2 , 20 x 1 and 5 x 4

NCERT Page No. 94

Bangles

There are 18 bangles on the rod. Meena is trying to group them. She can put them in groups of 2, 3, 6, 9 and 18 without any bangle being left.

(i) How many groups will she have if she makes groups of 1 bangle each? _____

(ii) Now complete the table, for different numbers of bangles. For each number see what different groups can be made.

 Number of bangles Different groups we can make 18 1, 2, 3, 6, 9, 18 24 1, 2, …………… 5 9 7 2 10 1 20 13 21

Answer.

(i) If she makes groups of 1 bangle each, she will get 18 groups.

(ii) Different groups that can be made with different number of bangles are given below:

 Number of bangles Different groups we can make 18 1, 2, 3, 6, 9, 18 24 1, 2, 3, 4, 6, 8, 12, 24 5 1, 5 9 1, 3, 9 7 1, 7 2 1, 2 10 1, 2, 5, 10 1 1 20 1, 2, 4, 5, 10, 20 13 1, 13 21 1, 3, 7, 21

NCERT Page No. 95

Fill the Chart

Complete the multiplication chart given here. Look at the green boxes in the chart. These show how we can get 12 by multiplying different numbers. 12 = 4 × 3, so 12 is a multiple of both 4 and 3. 12 is also a multiple of 6 and 2, as well as 12 and 1. We say 1, 2, 3, 4, 6, 12 are factors of 12.

(i) What are the factors of 10? _________ Can you do this from the chart?

(ii) What are the factors of 36? ________

(iii) Find out all the factors of 36 from the multiplication chart.

(iv) What is the biggest number for which you can find the factors form this chart?

(v) What can you do for numbers bigger than that?

Answer.

Multiplication chart can be filled as follows: (i) Factors of 10 are: 1, 2, 5 and 10.

(ii) Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Multiplication chart is as below:

 36 2         × 18  3 × 12  4 × 9   1 × 36  6 × 6

(iii) The biggest number for which we can find factors from the chart is 144.

(iv) For numbers larger than 144, we will reduce the number by division method and then find factors for smaller numbers using the table.

NCERT Page No. 96

1. Write the factors of 25 in the red circle and the factors of 35 in the blue circle. Which are the factors you have written in the common part (purple) of both circles? These are common factors of 25 and 35.

Answer.

Factors of 25 and 35 are written in the red and blue circles respectively as below: 1 and 5 are written in purple part as they are the common factors of 25 and 35.

2. Now write the factors of 40 in the red circle and 60 in the blue circle. Answer.

Factors of 40 and 60 are written in the red and blue circles respectively as follows: NCERT Page No. 97

Factor Tree

1. Look at the factor tree. Now can you make another tree like this? Answer.

Factor tree can be completed as follows: 2. In how many ways can you draw a factor tree for 24? Draw three of them below. Answer.

Factor tree for 24 can be drawn in following different ways: Tiling Problems

1. There is a garden in Anu’s house. In the middle of the garden there is a path. They decided to tile the path using tiles of length 2 feet, 3 feet and 5 feet.

The mason tiled the first row with 2 feet tiles, the second row with 3 feet tiles and the third row with 5 feet tiles. The mason has not cut any of the tiles. Then what is the shortest length of the path?

Answer.

Here the smallest common multiple of 2, 3 and 5 gives the shortest length of the path.

Multiples of 2: 2, 4, 6, 8, 10,12,14, 16,17, 18, 20, 22, 24, 26, 28, 30

Multiples of 3: 3, 6, 9,12, 15, 18, 21, 24, 27, 30

Multiples of 5: 5, 10, 15, 20, 25, 30

The smallest common multiple is 30.

So, the shortest length of the path is 30 m.

NCERT Page No. 98

2. Manoj has made a new house. He wants to lay tiles on the floor. The size of the room is 9 feet × 12 feet. In the market, there are three kinds of square tiles: 1 foot × 1 foot, 2 feet × 2 feet and 3 feet × 3 feet. Which size of tile should he buy for his room, so that he can lay it without cutting?

Answer.

Size of tile should be a factor of 9 and 12 both.

As 2 is not a factor of 9 feet which is the width of the room but 1 and 3 are factors of both 9 and 12.

Hence, Manoj can buy tiles of 1 foot x 1 foot or 3 feet x 3 feet.

3. Rani, Geetha and Naseema live near each other. The distance from their houses to the road is 90 feet. They decided to tile the path to the road. They all bought tiles of different designs and length. Rani bought the shortest tile, Geetha bought the middle sized one and Naseema bought the longest one. If they could tile the path without cutting any of the tiles, what is the size of the tiles each has bought? Suggest 3 different solutions. Explain how you get this answer.

Answer.

Length of the path = 90 feet

For the tiles to be tiled on the path without cutting, size of each tile should be a factor of 90.

Now 90 can be factorized as follows:

90 = 1 x 90

90 = 2 x 45

90 = 3 x 30

90 = 5 x 18

90 = 6 x 15

90 = 9 x 10

Hence possible tiles can be as follows: 1 x 1, 2 x 2, 3 x 3, 5 x 5, 6 x 6, etc.

Since Rani bought the shortest tile, Geetha bought the middle sized one and Naseema bought the longest one, different possible sizes can be selected as follows:

(i) Rani takes tiles of size = 1 foot × 1 foot

Geetha takes tiles of size = 2 feet × 2 feet

Naseema takes tiles of size = 3 feet × 3 feet

(ii)Rani takes tiles of size = 2 feet × 2 feet

Geetha takes tiles of size = 3 feet × 3 feet

Naseema takes tiles of size = 5 feet × 5 feet

(c) Rani takes tiles of size = 3 feet × 3 feet

Geetha takes tiles of size 5 feet × 5 feet

Naseema takes tiles of size 6 feet × 6 feet

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