Question

Tanvi is getting older and feels like she should donate her collection of stuffed animals to children who are less fortunate. She has 36 stuffed cats and 32 stuffed dogs, which she wants to divide into identical groups, with no stuffed animals left over. What is the greatest number of groups Tanvi can place her stuffed animals into?

Answer 1

4 number of groups each with 9 number of stuffed cats and 8 stuffed dogs.

Explanation:

Given that:

Number of stuffed cats = 36

Number of stuffed dogs = 32

These are to divided in identical groups such that no stuffed animal is left over.

We have to find the largest number of groups so that Tanvi can place her stuffed animals into.

To find the largest number of such groups, we need to find the HCF (Highest Common Factor).

Let us factorize the two numbers i.e. 36 and 32. Then we will underline the common factors between the two numbers.

`36 = \underline{2* 2} * 3* 3\\32 = \underline{2* 2} * 2* 2* 2`

Therefore, HCF is
`2* 2 = 4`

Therefore, there can be 4 number of groups at the most so that no stuffed animals is left over.

Each group will have
`\frac{36}4` = 9 number of stuffed cats and

`(32)/(4)` = 8 number of stuffed dogs.