Find the HCF of he numbers in each of the following , using the prime factorization method :
272, 425

Answer

To find the HCF (Highest Common Factor) of the numbers 272 and 425 using the prime factorization method, we will follow these steps:

### Step 1: Prime Factorization of 272
- Start dividing 272 by the smallest prime number, which is 2.
- 272 ÷ 2 = 136
- 136 ÷ 2 = 68
- 68 ÷ 2 = 34
- 34 ÷ 2 = 17
- 17 is a prime number, so we stop here.

The prime factorization of 272 is:
\[ 272 = 2^4 \times 17^1 \]

### Step 2: Prime Factorization of 425
- Start dividing 425 by the smallest prime number, which is 5.
- 425 ÷ 5 = 85
- 85 ÷ 5 = 17
- 17 is a prime number, so we stop here.

The prime factorization of 425 is:
\[ 425 = 5^2 \times 17^1 \]

### Step 3: Identify Common Factors
- Now we will look for the common prime factors in both factorizations:
- For 272: \( 2^4 \times 17^1 \)
- For 425: \( 5^2 \times 17^1 \)

The only common prime factor is \( 17^1 \).

### Step 4: Determine the HCF
- The HCF is the product of the lowest powers of the common prime factors.
- Since the only common prime factor is 17, the HCF is:
\[ \text{HCF} = 17^1 = 17 \]

### Final Answer
The HCF of 272 and 425 is **17**.

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