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

Solution:-

If Meena makes groups of 1 bangle each, she will get 18 groups.

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

Solution:-

Solution:-

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

Solution:-

From the chart, factors of 10 are 1, 2, 5 and 10.

(ii) What are the factors of 36?

Solution:-

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

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

Solution:-

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

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

Solution:-

From the multiplication chart, 144 is the biggest number for which we can find the factors.

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

Solution:-

First, we will extend the multiplication chart and then complete the chart.

Solution:-

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

Solution:-

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

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

Solution:-

(iv) What are the factors written in the common (purple) part of the circle? Which is the biggest common factor of 40 and 60?

Solution:-

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

20 is the biggest common factor of 40 and 60.

Solution:-

(ii) In how many ways can you draw a factor tree for 24? Draw three of them below.

Solution:-

Solution:-

From the question, it is given that 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.

So, now we have to find the LCM of 2, 3 and 5.

The LCM of 2, 3, and 5 is 30.

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

(ii) Manoj has a new house. He has 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?

Solution:-

From the question, it is given that the size of the room is 9 feet × 12 feet.

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

Here, 2 is not a factor of the width of the room, i.e. 9 feet, so Manoj cannot lay 2 feet × 2 feet tiles.

1 and 3 are the factors of 3 and 9.

Therefore, Monoj can buy 1 foot × 1 foot and 3 feet × 3 feet so that he can lay it without cutting.

(iii)

Rani, Geetha and Naseema live near each other. The distance from their house to the road is 90 feet. They decided to tile the path to the road. They all bought tiles of different designs and lengths. 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.

Solution:-

From the question, the distance from their house to the road is 90 feet.

Factors of 90 are 1, 2, 3, 5, 6, 9 etc.

Then, possible sizes of tiles are 1 foot × 1 foot, 2 feet × 2 feet, 3 feet × 3 feet, 5 feet × 5 feet, 6 feet × 6 feet and 9 feet × 9 feet etc.

Then the size of the tiles each has bought are,

(i) Rani 1 foot × 1 foot

Geetha 2 feet × 2 feet

Naseema 3 feet × 3 feet

(ii) Rani 2 feet × 2 feet

Geetha 3 feet × 3 feet

Naseema 5 feet × 5 feet

(iii) Rani 3 feet × 3 feet

Geetha 5 feet × 5 feet

Naseema 6 feet × 6 feet