Answer :
Answer:
To find the prime factors of 272 using the short division method, we divide the number by the smallest prime numbers until we can no longer divide evenly. Here’s the step-by-step process:
1. **Divide by 2 (the smallest prime number):**
\[
272 \div 2 = 136
\]
Prime factor: \(2\)
2. **Divide by 2 again:**
\[
136 \div 2 = 68
\]
Prime factor: \(2\)
3. **Divide by 2 again:**
\[
68 \div 2 = 34
\]
Prime factor: \(2\)
4. **Divide by 2 again:**
\[
34 \div 2 = 17
\]
Prime factor: \(2\)
5. **Divide by 17 (since 17 is a prime number):**
\[
17 \div 17 = 1
\]
Prime factor: \(17\)
So, the prime factorization of 272 is:
\[
2 \times 2 \times 2 \times 2 \times 17
\]
Or, using exponents:
\[
2^4 \times 17
\]
Thus, the prime factors of 272 are \( \boxed{2^4 \times 17} \).
Step-by-step explanation:
2 272
2. 136
2. 68
2. 34
2. 17
17. 17
1
hence prime factor of 272 is 2×2×2×2×2×17