GCF of 21/81, 88/27, 77/54
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/81, 88/27, 77/54 i.e 1/162 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/81, 88/27, 77/54.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 21/81,88/27,77/54?
Given fractions are 21/81,88/27,77/54
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 21/81,88/27,77/54, numerators are 21,88,77
Denominators are 81,27,54
The GCF of 21,88,77 is 1 .
LCM of 81,27,54 is 162.
The greatest common factor of 21/81,88/27,77/54 = [GCF of 21,88,77]/[LCM of 81,27,54]= 1/162
Therefore, the GCF of 21/81,88/27,77/54 is 1/162.
To find the highest common factor of 21,88,77, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88
The factors of 77 are 1, 7, 11, 77
The HCF of 21,88,77 is 1.
Lets's calculate GCF of 21,88,77
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,88,77 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 88
:1,2,4,8,11,22,44,88
Now, list down the factors of 77
:1,7,11,77
Greatest Common Factor
We found the factors 21,88,77 . The biggest common factor number is the GCF number.
So the greatest common factor 21,88,77 is 1.
Lets's calculate LCM of 81,27,54
| 3 | 81, 27, 54 |
| 3 | 27, 9, 18 |
| 3 | 3, 9, 6 |
| 1, 3, 2 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 1 x 3 x 2 = 162
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/162
Therefore, the GCF of Fractions 21/81,88/27,77/54 is 1/162
Least Common Multiple of 81,27,54 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 81,27,54 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,27,54) = 27
common factors(in case of two or more numbers have common factors) = 27
GCF(81,27,54) x common factors =27 x 27 = 729
LCM(81,27,54) = ( 81 × 27 × 54 ) / 729
LCM(81,27,54) = 118098 / 729
LCM(81,27,54) = 162
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FAQs on GCF of Fractions of 21/81, 88/27, 77/54
1. What is the HCF of 21,88,77?
The HCF of 21,88,77 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 21/81, 88/27, 77/54?
Answer: GCF of Numerators as per given numbers 21/81, 88/27, 77/54 is
GCF of Numerators i.e. for 21,88,77 is 1
LCM of denominators i.e. for 81,27,54 is 162.
Thus, GCF of Fractions is 1/162.Finally, GCF of Fractions for 21/81, 88/27, 77/54 is 1/162.