To find the highest common factor (HCF) of the numbers 10, 24, and 50, we can follow these steps:
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Find the prime factorization of each number:
- 10: \( 2 \times 5 \)
- 24: \( 2^3 \times 3 \)
- 50: \( 2 \times 5^2 \)
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Identify the common prime factors:
- The only prime factor common to all three numbers is \( 2 \).
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Determine the lowest power of the common prime factors:
- The power of \( 2 \) in each factorization is:
- For 10: \( 2^1 \)
- For 24: \( 2^3 \)
- For 50: \( 2^1 \)
- The lowest power of \( 2 \) among them is \( 2^1 \).
- The power of \( 2 \) in each factorization is:
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Calculate the HCF:
- Therefore, the HCF of 10, 24, and 50 is \( 2^1 = 2 \).
Thus, the highest common factor of 10, 24, and 50 is 2.