The Highest Common Factor (HCF) of 55 and 210 is 5.
Understanding the Highest Common Factor (HCF)
The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. Finding the HCF is a fundamental concept in number theory, useful in simplifying fractions and solving various mathematical problems.
Finding the HCF of 55 and 210
There are several methods to find the HCF of two numbers, such as the prime factorization method or the Euclidean algorithm. The reference provided utilizes the prime factorization approach to determine the HCF.
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Prime Factorization: This method involves breaking down each number into its prime factors.
- The prime factors of 55 are 5 and 11. (Since 55 = 5 × 11)
- The prime factors of 210 are 2, 3, 5, and 7. (Since 210 = 2 × 3 × 5 × 7)
We can list these for clarity:
- Prime Factors of 55: {5, 11}
- Prime Factors of 210: {2, 3, 5, 7}
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Identifying Common Prime Factors: Next, we look for prime factors that appear in both lists.
- Comparing the sets {5, 11} and {2, 3, 5, 7}, the only prime factor common to both 55 and 210 is 5.
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Determining the HCF: The HCF is the product of all common prime factors.
According to the information from BYJU's, "The only common prime factor of 210 and 55 is 5. Hence, the HCF of 210 and 55 is 5."
Since 5 is the only prime factor that 55 and 210 share, the HCF is 5.
The HCF of 55 and 210 is indeed 5.
