Question

hcf of 2/3,8/9,16/81

Answer 1

$hi \: dear \\ your \: answer \: is \: here$
HCF = Factors of 2=1,2
8=1,4,8
16=1,2,4,8 and 16
Common=1,2
HCF=2

LCM of 3 ,9 and 81=81

Answer is
$\frac{2}{81}$
HCF of
$\frac{2}{3} . \frac{8}{9} . \frac{16}{81} is \: \frac{2}{81}$
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Answer 2

• HCF of given fractions is equal to 2/81 .

To Find :-

• HCF of 2/3 , 8/9 and 16/81 .

Formula used :-

• HCF of fractions = HCF of numerators / LCM of denominators .

Solution :-

As we can see that, given fractions :-

→ 2/3 :-

• Numerator = 2
• Denominator = 3

→ 8/9 :-

• Numerator = 8
• Denominator = 9

→ 16/81 :-

• Numerator = 16
• Denominator = 81

So,

→ HCF of given fractions = HCF of numerators of given fractons / LCM of denominators of given fractions .

→ HCF (2/3, 8/9, 16/81) = [HCF(2, 8, 16) / LCM (3, 9, 81)] ------- Equation (1)

Finding HCF of numerators first by prime factorization method we get :-

→ 2 = 1 × 2

→ 8 = 1 × 2 × 2 × 2

→ 16 = 1 × 2 × 2 × 2 × 2

So,

→ HCF(2, 8, 16) = 1 × 2 = 2 --------- Equation (2)

Similarly, finding LCM of denominators first by prime factorization method we get :-

→ 3 = 1 × 3

→ 9 = 1 × 3 × 3

→ 81 = 1 × 3 × 3 × 3 × 3

So,

→ LCM(3, 9, 81) = 1 × 3 × 3 × 3 × 3 = 81 ---- Equation (3)

therefore, putting values of Equation (2) and Equation (3) in Equation (1) we get,

→ HCF (2/3, 8/9, 16/81) = 2/81 (Ans.)

Hence, we can conclude that, the HCF of 2/3, 8/9, 16/81 is equal to 2/81 .

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