HCF of Fractions Calculation
The question asks for the Highest Common Factor (HCF) of the fractions $\frac{2}{3}$, $\frac{3}{4}$, and $\frac{5}{6}$.
Finding HCF of Fractions
To find the HCF of multiple fractions, we use the formula:
$ \text{HCF}\left(\frac{a}{b}, \frac{c}{d}, \frac{e}{f}\right) = \frac{\text{HCF}(a, c, e)}{\text{LCM}(b, d, f)} $
Here, $a, c, e$ are the numerators and $b, d, f$ are the denominators.
Step 1: Identify Numerators and Denominators
- Numerators: 2, 3, 5
- Denominators: 3, 4, 6
Step 2: Calculate HCF of Numerators
We need to find the HCF of 2, 3, and 5.
- Factors of 2: 1, 2
- Factors of 3: 1, 3
- Factors of 5: 1, 5
- The highest common factor is 1.
Therefore, HCF(2, 3, 5) = 1.
Step 3: Calculate LCM of Denominators
We need to find the Least Common Multiple (LCM) of 3, 4, and 6.
- Prime factorization of 3 = 3
- Prime factorization of 4 = $2^2$
- Prime factorization of 6 = 2 $\times$ 3
- LCM(3, 4, 6) = $2^2 \times 3 = 4 \times 3 = 12$.
Therefore, LCM(3, 4, 6) = 12.
Step 4: Calculate HCF of the Fractions
Using the formula from Step 1:
$ \text{HCF}\left(\frac{2}{3}, \frac{3}{4}, \frac{5}{6}\right) = \frac{\text{HCF}(2, 3, 5)}{\text{LCM}(3, 4, 6)} = \frac{1}{12} $
The HCF of the given fractions is $\frac{1}{12}$.
Similar Questions
- The numerator of a fraction is increased by $20\%$ and the denominator is decreased by $50\%$. If the resultant fraction is $\frac{5}{6}$, then what will be the original fraction?
- $1.236576576...$
can be written in the form of: - What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
- What is the positive difference between $\frac{5}{16}$ and its reciprocal?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- Solve the following:
$(0.\overline{5} + 0.\overline{6} + 0.\overline{7} + 0.\overline{8}) = ?$ - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
Important Questions from Fractions
Which fraction among the following is the least ?
\(\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}\)
Find the value of the following expression:
\(\frac{{3 \div 1 \times 2 + 5 - 2}}{{3 \times 3 - 2}}\)
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
