Question
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Answer
The HCF of 8 and 21 is 1.
Solution
1. Write down the factors of \(8\):
\(\{1, 2, 4, 8\}\)
2. Write down the factors of \(21\):
\(\{1, 3, 7, 21\}\)
3. Identify the common factors:
The only common factor is \(1\).
4. Thus, the Highest Common Factor (HCF) is:
\(\boxed{1}\)
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Simplify this solution The Deep Dive
The highest common factor (HCF) of 8 and 21 is 1. This means that these two numbers are relatively prime, as they share no common factors other than 1. It's always interesting to note that when you have numbers that are not multiples of each other, their HCF tends to be 1! If you're ever trying to find the HCF of larger numbers, one fun method is to use the prime factorization technique. Break each number down into its prime factors and then identify the smallest power of the common primes. For 8 (which is 2³) and 21 (which is 3¹ and 7¹), there's nothing in common, leading us right back to our HCF of 1!
