Shalvi wants to organize her birthday party. She is very health conscious, thus shedecided to serve fruits only. She has 36 apples and 60 bananas at home and decided toserve them. She want to distribute fruits among guests. She does not want todiscriminate among guests so she decided to distribute equally among all.

To distribute the fruits equally among the guests, we need to determine the number of guests first. Since Shalvi wants to serve only fruits at her birthday party, we can assume that each guest will receive a combination of apples and bananas.

To find the number of guests, we need to divide the total number of fruits by the number of fruits each guest will receive. Since Shalvi wants to distribute the fruits equally, we can assume that each guest will receive the same number of fruits.

Let's assume that each guest will receive x number of fruits. Therefore, the total number of guests can be calculated by dividing the total number of fruits (36 apples + 60 bananas) by x.

Total number of fruits = 36 apples + 60 bananas = 96 fruits

Let's divide the total number of fruits by x:

96 fruits / x = number of guests

Since Shalvi wants to distribute the fruits equally among all the guests, we need to find a value of x that evenly divides 96.

To find the factors of 96, we can start by dividing it by 2:

96 / 2 = 48

48 is still divisible by 2:

48 / 2 = 24

24 is also divisible by 2:

24 / 2 = 12

12 is divisible by 2:

12 / 2 = 6

6 is divisible by 2:

6 / 2 = 3

3 is not divisible by 2, so we need to try dividing it by the next prime number, which is 3:

3 / 3 = 1

Now we have found all the prime factors of 96: 2, 2, 2, 2, 2, 3.

To find the total number of guests, we need to multiply these prime factors together:

2 * 2 * 2 * 2 * 2 * 3 = 96

Therefore, the total number of guests at Shalvi's birthday party will be 96.

Now that we know the number of guests, we can distribute the fruits equally among them. Each guest will receive a combination of apples and bananas. To determine the number of fruits each guest will receive, we can divide the total number of fruits (96) by the number of guests (96):

96 fruits / 96 guests = 1 fruit per guest

Therefore, each guest will receive 1 fruit, either an apple or a banana.

In summary, Shalvi has a total of 36 apples and 60 bananas. She wants to distribute them equally among the guests at her birthday party. After finding the total number of guests (96), we determined that each guest will receive 1 fruit, either an apple or a banana.