HCF of 105,90,195,215=

Options

A. 5
B. 10
C. 15
D. 25

Answer

To find the Highest Common Factor (HCF) of the numbers 105, 90, 195, and 215, we will follow these steps:

### Step 1: Prime Factorization of Each Number
We will start by performing the prime factorization of each number.

1. **Prime Factorization of 105:**
- Divide by 5: \( 105 \div 5 = 21 \)
- Divide 21 by 3: \( 21 \div 3 = 7 \)
- So, \( 105 = 5 \times 3 \times 7 \)

2. **Prime Factorization of 90:**
- Divide by 2: \( 90 \div 2 = 45 \)
- Divide 45 by 3: \( 45 \div 3 = 15 \)
- Divide 15 by 3: \( 15 \div 3 = 5 \)
- So, \( 90 = 2 \times 3^2 \times 5 \)

3. **Prime Factorization of 195:**
- Divide by 3: \( 195 \div 3 = 65 \)
- Divide 65 by 5: \( 65 \div 5 = 13 \)
- So, \( 195 = 3 \times 5 \times 13 \)

4. **Prime Factorization of 215:**
- Divide by 5: \( 215 \div 5 = 43 \)
- So, \( 215 = 5 \times 43 \)

### Step 2: List the Prime Factors
Now we have the prime factorizations:
- \( 105 = 5 \times 3 \times 7 \)
- \( 90 = 2 \times 3^2 \times 5 \)
- \( 195 = 3 \times 5 \times 13 \)
- \( 215 = 5 \times 43 \)

### Step 3: Identify Common Prime Factors
Next, we will identify the common prime factors from all the numbers:
- The only common prime factor among all four numbers is **5**.

### Step 4: Determine the HCF
Since the only common prime factor is 5, the HCF of 105, 90, 195, and 215 is:
- **HCF = 5**

### Final Answer
The HCF of 105, 90, 195, and 215 is **5**.

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