Three farmers have 165 kg, 190 kg and 210 kg of wheat respectively. Find the maximum capacity of a bag such that the quantity of wheat can be packed in exact number of bags.

Options

A. 15 kg
B. 50 kg
C. 45 kg
D. 5 kg

Answer

To find the maximum capacity of a bag such that the quantities of wheat from the three farmers can be packed into an exact number of bags, we need to determine the highest common factor (HCF) of the weights of wheat they have.

Let's solve the problem step by step:

### Step 1: List the weights of wheat
The weights of wheat from the three farmers are:
- Farmer 1: 165 kg
- Farmer 2: 190 kg
- Farmer 3: 210 kg

### Step 2: Factorize each weight
We need to factor each of these weights into their prime factors.

1. **Factorizing 165 kg:**
- 165 = 3 × 5 × 11

2. **Factorizing 190 kg:**
- 190 = 2 × 5 × 19

3. **Factorizing 210 kg:**
- 210 = 2 × 3 × 5 × 7

### Step 3: Identify the common factors
Now, we will identify the common prime factors from the factorizations we obtained:

- From 165: 3, 5, 11
- From 190: 2, 5, 19
- From 210: 2, 3, 5, 7

The only common prime factor among all three weights is **5**.

### Step 4: Determine the HCF
Since 5 is the only common factor present in all three numbers, the highest common factor (HCF) is:

**HCF = 5 kg**

### Step 5: Conclusion
The maximum capacity of a bag such that the quantities of wheat can be packed in an exact number of bags is **5 kg**.

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