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Answer
The HCF of 63 and 343 is 7.
Solution
1. Write the prime factorization of \(63\):
- \(63 = 3^2 \times 7\).
2. Write the prime factorization of \(343\):
- \(343 = 7^3\).
3. Identify the common prime factor:
- The only common prime factor is \(7\).
4. Take the lowest power of each common prime factor:
- For \(7\), the lowest power is \(7^1 = 7\).
Thus, the highest common factor (HCF) of \(63\) and \(343\) is \(7\).
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Simplify this solution Mind Expander
Did you know that the highest common factor (HCF) is a key concept in number theory that dates back to ancient times? The process of finding the HCF has roots in the work of mathematicians like Euclid, who developed the Euclidean algorithm over 2,000 years ago. This algorithm not only helps in finding the HCF, but also lays the groundwork for further mathematical discoveries! To find the HCF of 63 and 343, you can use prime factorization. Since 63 equals 3² × 7, and 343 equals 7³, their only common factor is 7. Thus, the HCF of 63 and 343 is 7! This technique can be applied to any set of numbers to uncover their greatest common ally!
