What are the factors of $36?$

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

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 $35.$

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

What are the factors written in the common (purple) part of the circle? Which is the biggest common factor of $40$ and $60?\mathrm{}$

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.

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(in feet)?

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