A gardener has 200 roses and 180 chameli flowers. It is said to him that he should make the garlands of roses and chameli flowers reportedly. Find the maximum no. of flowers from which the garlands can be made and no flower left behind.

Options

A. 50
B. 30
C. 20
D. 10

Answer

To solve the problem of how many garlands can be made from 200 roses and 180 chameli flowers without leaving any flowers behind, we need to find the Highest Common Factor (HCF) of the two numbers.

### Step-by-Step Solution:

**Step 1: Identify the quantities of flowers.**
- The gardener has 200 roses and 180 chameli flowers.

**Step 2: Factorize the numbers.**
- We will factor both numbers to find their prime factors.

For 200:
- 200 = 2 × 100
- 100 = 2 × 50
- 50 = 2 × 25
- 25 = 5 × 5
- Therefore, 200 = 2^3 × 5^2.

For 180:
- 180 = 2 × 90
- 90 = 2 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- Therefore, 180 = 2^2 × 3^2 × 5.

**Step 3: Identify the common factors.**
- Now we will identify the common prime factors from the factorization:
- For 200: 2^3 × 5^2
- For 180: 2^2 × 3^2 × 5

**Step 4: Calculate the HCF.**
- The HCF is found by taking the lowest power of all common prime factors:
- For 2: The minimum power is 2 (from 2^2).
- For 5: The minimum power is 1 (from 5^1).

Therefore, HCF = 2^2 × 5^1 = 4 × 5 = 20.

**Step 5: Conclusion.**
- The maximum number of flowers that can be used to make garlands, with no flowers left behind, is 20.

### Final Answer:
The maximum number of flowers in each garland is **20**.

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