Preeti baked `352` butter cream cookies, `448` cashew nut cookies and `736` choconut cookies to sell at her stall in a fair. She wants to pack the cookies in packets so that each packet has the same number of cookies of the same kind. If she wants to pack the largest number of cookies possible in each packet, how many packets will she need to pack ? Also find the number of packets of each kind of cookies

Options

A. Total number of packets `-48`
Butter cream cookies `- 11`
Cashew nut cookies `-14`
Choconut cookies `-23`
B. Total number of packets `-48`
Butter cream cookies `- 11`
Cashew nut cookies `-23`
Choconut cookies `-14`
C. Total number of packets `-38`
Butter cream cookies `- 9`
Cashew nut cookies `-6`
Choconut cookies `-23`
D. Total number of packets `-38`
Butter cream cookies `- 11`
Cashew nut cookies `-14`
Choconut cookies `-13`

Answer

To solve the problem, we need to find the highest common factor (HCF) of the number of cookies Preeti baked: 352 butter cream cookies, 448 cashew nut cookies, and 736 choconut cookies. This will tell us how many cookies can be packed in each packet while ensuring that each packet has the same number of cookies of the same kind.

### Step-by-Step Solution:

**Step 1: Find the HCF of 352, 448, and 736.**

To find the HCF, we can use the division method.

1. **Divide 736 by 448:**
- 736 ÷ 448 = 1 (remainder 288)
- So, 736 = 448 × 1 + 288

2. **Now divide 448 by 288:**
- 448 ÷ 288 = 1 (remainder 160)
- So, 448 = 288 × 1 + 160

3. **Now divide 288 by 160:**
- 288 ÷ 160 = 1 (remainder 128)
- So, 288 = 160 × 1 + 128

4. **Now divide 160 by 128:**
- 160 ÷ 128 = 1 (remainder 32)
- So, 160 = 128 × 1 + 32

5. **Now divide 128 by 32:**
- 128 ÷ 32 = 4 (remainder 0)
- So, 128 = 32 × 4 + 0

Since the remainder is now 0, the last non-zero remainder is the HCF. Thus, the HCF of 352, 448, and 736 is **32**.

**Step 2: Calculate the number of packets for each type of cookie.**

Now that we know the HCF is 32, we can find out how many packets of each type of cookie Preeti can pack.

1. **For butter cream cookies:**
- Number of packets = 352 ÷ 32 = 11

2. **For cashew nut cookies:**
- Number of packets = 448 ÷ 32 = 14

3. **For choconut cookies:**
- Number of packets = 736 ÷ 32 = 23

**Step 3: Calculate the total number of packets.**

Now, we add the number of packets for each type of cookie:

Total packets = 11 (butter cream) + 14 (cashew nut) + 23 (choconut) = 48 packets.

### Final Answer:
Preeti will need a total of **48 packets** to pack all the cookies, with **32 cookies** in each packet.

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