To find the Highest Common Factor (HCF) of the two fractions \( \frac{8}{30} \) and \( \frac{12}{36} \), we first determine the HCF of the numerators (8 and 12) and the HCF of the denominators (30 and 36).
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Finding the HCF of the numerators (8 and 12):
- The factors of 8 are: \( 1, 2, 4, 8 \)
- The factors of 12 are: \( 1, 2, 3, 4, 6, 12 \)
- The common factors are: \( 1, 2, 4 \)
- Therefore, the HCF of 8 and 12 is \( 4 \).
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Finding the HCF of the denominators (30 and 36):
- The factors of 30 are: \( 1, 2, 3, 5, 6, 10, 15, 30 \)
- The factors of 36 are: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- The common factors are: \( 1, 2, 3, 6 \)
- Therefore, the HCF of 30 and 36 is \( 6 \).
Now, we can summarize the results:
- HCF of the numerators (8 and 12) = 4
- HCF of the denominators (30 and 36) = 6
The overall HCF of the fractions \( \frac{8}{30} \) and \( \frac{12}{36} \) can be represented as the fraction \( \frac{4}{6} \), which can be simplified to \( \frac{2}{3} \).
Thus, the Highest Common Factor of the two fractions is: \(\frac{2}{3}\).