GCF of 28/61, 54/78, 48/129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/61, 54/78, 48/129 i.e 2/204594 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/61, 54/78, 48/129.
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 28/61,54/78,48/129?
Given fractions are 28/61,54/78,48/129
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 28/61,54/78,48/129, numerators are 28,54,48
Denominators are 61,78,129
The GCF of 28,54,48 is 2 .
LCM of 61,78,129 is 204594.
The greatest common factor of 28/61,54/78,48/129 = [GCF of 28,54,48]/[LCM of 61,78,129]= 2/204594
Therefore, the GCF of 28/61,54/78,48/129 is 2/204594.
To find the highest common factor of 28,54,48, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The HCF of 28,54,48 is 2.
Lets's calculate GCF of 28,54,48
| 2 | 28, 54, 48 |
| 14, 27, 24 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 28,54,48 By Matching Biggest Common Factor Method
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Greatest Common Factor
We found the factors 28,54,48 . The biggest common factor number is the GCF number.
So the greatest common factor 28,54,48 is 2.
Lets's calculate LCM of 61,78,129
| 3 | 61, 78, 129 |
| 61, 26, 43 |
∴ So the LCM of the given numbers is 3 x 61 x 26 x 43 = 204594
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/204594
Therefore, the GCF of Fractions 28/61,54/78,48/129 is 2/204594
Least Common Multiple of 61,78,129 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 61,78,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(61,78,129) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(61,78,129) x common factors =1 x 3 = 3
LCM(61,78,129) = ( 61 × 78 × 129 ) / 3
LCM(61,78,129) = 613782 / 3
LCM(61,78,129) = 204594
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FAQs on GCF of Fractions of 28/61, 54/78, 48/129
1. What is the HCF of 28,54,48?
The HCF of 28,54,48 is 2
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 28/61, 54/78, 48/129?
Answer: GCF of Numerators as per given numbers 28/61, 54/78, 48/129 is
GCF of Numerators i.e. for 28,54,48 is 2
LCM of denominators i.e. for 61,78,129 is 204594.
Thus, GCF of Fractions is 2/204594.Finally, GCF of Fractions for 28/61, 54/78, 48/129 is 2/204594.