Be My Multiple, I’ll be Your Factor JKBOSE Solutions

“Be My Multiple, I’ll be Your Factor” is Chapter 6 from Merry Math V for students of Class 5th of JKBOSE. This post is about Be My Multiple, I’ll be Your Factor JKBOSE Solutions. In a previous post, you read about Does It Look The Same Chapter 5 Class 5 JKBOSE Solutions. Let’s get started:

Be My Multiple, I’ll be Your Factor JKBOSE Solutions

Page No. 91 Solutions.

The Mouse and the Cat

The hungry cat is trying to catch Jerry the mouse. Jerry is now on the 14th step and it can jump two steps at a time. The cat is on the third step. She can jump three steps at a time. If the mouse reaches 28 it can hide in the hole. Find out whether the mouse can get away safely!

a) The steps on which the mouse jumps ______

Ans. The steps on which the mouse jumps are 16, 18, 20, 22, 24, 26, and 28.

b) The steps on which the cat jumps ______

Ans. The steps on which the cat jumps are 6, 9, 12, 15, 18, 21, 24, and 27.

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

Ans. The cat and mouse jump on the steps of 18 and 24.

d) Can the mouse get away?

Ans. Yes, the mouse can 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?

Ans. In this case,

The steps on which the cat jumps are 10, 15, 20 and 25.

The steps on which the mouse jumps are 12, 16, 20, 24 and 28.

No, the mouse cannot get away in this case, the cat will get the mouse on 3^rd jump because both cat and mouse jump on step 20 in their 3^rd jump.

Page No. 92 Solutions.

Who is Pappu waiting for?

Pappu cat is waiting for somebody. Do you know for whom he is waiting? There is a trick to find out.

Mark with a red dot all the numbers which can be divided by 2.

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

Ans.

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

Ans. The boxes which have dots of all three colours are 12, 24, 36, 48, and 60.

What are the letters on top of these boxes?

Ans. The letters on top of these boxes are M, O, U, S, and E.

Write those letters below in order.

Ans. MOUSE

Page No. 93 Solutions.

Meow Game

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 a 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’?

Ans. The numbers which replace with ‘Meow’ and multiples of 3 are, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45 and so on.

We say these numbers are multiples of 3. Play the game by changing the number to 4. Now, which number did you replace with ‘Meow’? These numbers are the multiples of 4.

Ans. The numbers which replace with ‘Meow’ are, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, and so on.

Write any ten multiples of 5.

Ans. The ten multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50.

Page No. 94 Solutions.

Dice Game

Throw two dice together. What are the numbers that turn up on the faces of the dice?

Mark a two-digit number using them. If it is a multiple 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.

Ans.

Page No. 95 Solutions.

Common Multiples

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.

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?

Ans.

Which is the smallest among these common multiples? _____________

Ans. 15 is the smallest among these common multiples.

Repeat the game using the numbers 2 and 7.

Ans.

Which is the smallest among these common multiples? _____________

Ans. 14 is the smallest among these common multiples.

Repeat the game by putting the multiples of 4, 6 and 5 in the circle.

Ans.

Page No. 96 Solutions.

What common multiples of 5 and 6 did you write in the green part?

Ans. 30, 60 and 90 are the common multiples of 5 and 6 are written in green part.

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

Ans. 12, 24, 36, 48, 60 and 72 are the common multiples of 4 and 6 are written in orange part.

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

Ans. The common multiples of 4, 6 and 5 are written in the grey part.

What is the smallest common multiple of 4, 6 and 5?

Ans. The smallest common multiple of 4, 6 and 5 is 60.

Puzzle

Tamarind seeds

Sumiya 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 Sumiya had?

Ans. First of all, we find out the smallest common multiple of 4, 5 and 6. The smallest common multiple of 4, 5 and 6 is 60.

But each time, Sumiya found that one seed was left over. So, the required number is 60 +1 = 61.

Hence, the smallest number of seeds Sumiya had is 61.

Page No. 97 Solutions.

More tamarind seeds

Ammini arranges 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?

Ans. First of all, write all the common factors of 12.

1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12 and 4 × 3 = 12.

So, we can make three different types of rectangles using 12 seeds. These are as under;

If there are 15 tamarind seeds, how many rectangles can you make?

Ans. The common factors of 15 are 1 × 15, 3 × 5 = 15 and 5 × 3 = 15.

So, we can make two different types of rectangles using 15 seeds.

Colouring the Grid

In the grid here, a rectangle made of 20 boxes is drawn. The width of this rectangle is 2 boxes.

What is its length?

Ans. The length of a rectangle is 10 boxes.

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

Ans.

What is the length and width of the rectangle of the rectangle you coloured?

Ans. The length of the rectangle is 5 boxes and the width is 4 boxes.

In how many ways can you colour a rectangle of 20 boxes?

Ans. We can colour a rectangle of 20 boxes in 3 ways.

Colour them all in the grid, and write the length and width of each rectangle you have coloured.

Ans. In rectangle 1, the length of the rectangle is 20 boxes and the width is 1 box.

In rectangle 2, the length of the rectangle is 4 boxes and the width is 5 boxes.

In rectangle 3, the length of the rectangle is 5 boxes and the width is 4 boxes.

Page No. 98 Solutions.

Bangles

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

How many groups will she have if she makes groups of 1 bangle each?

Ans. She will have 18 groups of 1 bangle each.

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

Ans.

Page No. 99 -100 Solutions.

Fill the Chart

Complete the multiplication chart given here.

Ans.

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, and 12 are factors of 12.

What are the factors of 10? _____________

Ans. The factors of 10 are 1, 2, 5, and 10.

Can you do this from the chart?

Ans. Yes, we can do this from the above chart.

What are the factors of 36? ____________

Ans. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36

Find out all the factors of 36 from the multiplication chart.

Ans. From the multiplication chart, the factors of 36 are 1, 2, 3, 4, 6, 9 and 12.

What is the biggest number for which you can find the factors from this chart?

Ans. 144 is the biggest number for which we can find the factors from this multiplication chart.

What can you do for numbers bigger than that?

Ans. We can extend the multiplication chart and complete it to get factors of numbers bigger than 144.

Common Factors

Write the factors of 25 in the red circle and the factors of 35 in the blue circle.

Ans.

Which are the factors of 25 and 35 you have written in the common part (purple) of both circles? 

Ans. 1 and 5 are the common factors of 25 and 35 written in the common part (purple).

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

Ans.

Page No. 101 Solutions.

What are the factors written in the common (purple) part of the circle?

Ans. The factors written in the common (purple) part of the circle are 1, 2, 4, 5, 10 and 20.

Which is the biggest common factor of 40 and 60?

Ans. 20 is the biggest common factor of 40 and 60.

Factor Tree

(a) Look at the factor tree. Now can you make another tree like this?

In how many ways can you draw a factor tree for 24?

Draw three of them below.

Ans.

Page No. 102 – 103 Solutions

Tilling Problems

1. There is a garden in Nazima’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. Then what is the shortest length of the path?

Ans. The shortest length of the path is the smallest common multiple of 2, 3, and 5

Therefore, the shortest length of the path = 2 × 3 × 5 = 30 feet.

2. Irfan 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 tiles should he buy for his room, so that he can lay it without cutting?

Ans. The size of the room is 9 feet × 12 feet.

The sizes of the tiles available in the market are 1 foot ×1 foot, 2 feet × 2 feet and 3 feet × 3 feet.

The size of the tiles Irfan can lay in the room without should be the common factor of 9 and 12.

Therefore, the tiles of sizes 1 foot ×1 foot, and 3 feet × 3 feet can be laid on the floor without cutting.

3. Asma, Sumaira, and Rukaiya 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 lengths. Asma bought the shortest tile, Sumaira bought the middle-sized one and Rukaiya 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.

Ans. From the question, the distance from their house to the road is 90 feet. Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, and 45.

Here are three different solutions:

Solution 1:

• Rani: 1 foot
• Geetha: 2 feet
• Naseema: 3 feet

Explanation:

• 1, 2 and 3 are all factors of 90.

• 90 ÷ 1 = 90 tiles for Rani
• 90 ÷ 2 = 45 tiles for Geetha
• 90 ÷ 3 = 30 tiles for Naseema

Solution 2:

• Rani: 5 feet
• Geetha: 6 feet
• Naseema: 9 feet

Explanation:

• 5, 6, and 9 are all factors of 90.
• 90 ÷ 5 = 18 tiles for Rani
• 90 ÷ 6 = 15 tiles for Geetha
• 90 ÷ 9 = 10 tiles for Naseema

Solution 3:

• Rani: 10 feet
• Geetha: 15 feet
• Naseema: 18 feet

Explanation:

• 10, 15, and 18 are all factors of 90.
• 90 ÷ 10 = 9 tiles for Rani
• 90 ÷ 15 = 6 tiles for Geetha
• 90 ÷ 18 = 5 tiles for Naseema

Now Let’s Do These

1. Write the factors of:a) 16 b) 28 c) 54  d) 80

Ans. Factors of 16 are 1, 2, 4, 8, and 16.

Factors of 28 are 1, 2, 4, 7, 14, and 28.

Factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

2. Write the common factors of:

(a) 9 and 15 (b) 18 and 21 (c) 27 and 54

Ans. (a) 9 and 15

Factors of 9 are 1, 3, and 9.

Factors of 15 are 1, 3, 5, and 15

Common factors of 9 and 15 are 1 and 3.

(b) 18 and 21

Factors of 18 are 1, 2, 3, 6, 9 and 18.

Factors of 21 are 1, 3, 7 and 21

Common factors of 18 and 21 are 1 and 3.

(c) 27 and 54

Factors of 27 are 1, 3, 9 and 27

Factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54

Common factors of 27 and 54 are 1, 3, 9, and 27

3. Write the first five multiples of:

(a) 3 (b) 5 (c) 9 (d) 11

Ans. a. The first five multiples of 3 are 3, 6, 9, 12, and 15.

25. The first five multiples of 5 are 5, 10, 15, 20, and 25.
26. The first five multiples of 9 are 9, 18, 27, 36, and 45.
27. The first five multiples of 11 are 11, 22, 33, 44, and 55.
28. Write the first two common multiples of:

(a) 5 and 6 (b) 4 and 3 (c) 4 and 8 (d) 3 and 5 (e) 3 and 7

Ans. (a) 5 and 6

Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 and so on….

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84 and so on…

The first two common multiples of 5 and 6 are 30 and 60.

(b) 4 and 3

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, and so on ….

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, and so on ….

The first two common multiples of 4 and 3 are 12 and 24

(c) 4 and 8

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, and so on ….

Multiples of 8 are 8, 16, 24, 32, 40, 48 56, 64, 72, 80, 88, 96, 102 and so on …

The first two common multiples of 4 and 8 are 8 and 16.

(d) 3 and 5

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, and so on ….

Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 and so on….

The first two common multiples of 3 and 5 are 15 and 30.

(e) 3 and 7

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, and so on ….

Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 and so on …

The first two common multiples of 3 and 7 are 21 and 42.

5. Which of the following numbers are divisible:

(a) By 2 (b) By 4 (c) By 5

4940, 940, 25280, 562, 496, 3625

Ans. The numbers 4940, 940, 25280, 562, and 496 are divisible by 2.

The numbers 4940, 940, 25280 and 496 are divisible by 4.

The numbers 4940, 940, 25280 and 3625 are divisible by 5.

6. Find the H.C.F of:

(a) 12 and 16 (b) 45 and 36 (c) 28 and 40 (d) 40 and 75 (e) 49 and 36

Ans. (a) 12 and 16

Factors of 12 are 1, 2, 3, 4, 6, and 12.

Factors of 16 are 1, 2, 4, 8, and 16.

The H.C.F of 12 and 16 is 4.

(b) 45 and 36

Ans. Factors of 45 are 1, 3, 5, 9, 15 and 45.

Factors of 36 are 1, 2, 3, 4, 9, 12, 18 and 36.

The H.C.F of 45 and 36 is 9

(c) 28 and 40

Ans. Factors of 28 are 1, 2, 4, 7, 14 and 28.

Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.

The H.C.F of 28 and 40 is 4.

(d) 40 and 75

Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.

Factors of 75 are 1, 3, 5, 15, 25 and 75.

The H.C.F of 40 and 75 is

(e) 49 and 36

Factors of 49 are 1, 7 and 49

Factors of 36 are 1, 2, 3, 4, 9, 12, 18 and 36.

The H.C.F of 49 and 36 is 1.

7. Find the L.C.M of:

(a) 3, 4 (b) 6, 9 (c) 12, 18 (d) 9, 15 (e) 7, 8

Ans. (a) 3, 4

Multiples of 3 are 3, 6, 9, 12, 15, 16, and so on.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on ….

L.C.M of 3, 4 is 12.

(b) 6, 9

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, and so on…

Multiples of 9 are 9, 18, 27, 36, 45, 54 and so on…

L.C.M of 6, 9 is 18.

(c) 12, 18

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108 and so on …

Multiples of 18 are 18, 36, 54, 72, 90, 108 and so on ….

L.C.M of 12, 18 is 36.

(d) 9, 15

Multiples of 9 are 9, 18, 27, 36, 45, 54, 63 and so on….

Multiples of 15 are 15, 30, 45, 60, 75, 90, 105 and so on ….

L.C.M of 9, 15 is 45.

(e) 7, 8

Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, and so on …

Multiples of 8 are 8, 16, 24, 32, 40, 48 56, 64, and so on …

L.C.M of 7, 8 is 56.

That’s it about Be My Multiple, I’ll be Your Factor JKBOSE Solutions. Hope it has helped. Do share your views about this post in the comments section below.