GCF of 77/66, 154/20, 129/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 77/66, 154/20, 129/578 i.e 1/190740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/66, 154/20, 129/578.
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 77/66,154/20,129/578?
Given fractions are 77/66,154/20,129/578
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 77/66,154/20,129/578, numerators are 77,154,129
Denominators are 66,20,578
The GCF of 77,154,129 is 1 .
LCM of 66,20,578 is 190740.
The greatest common factor of 77/66,154/20,129/578 = [GCF of 77,154,129]/[LCM of 66,20,578]= 1/190740
Therefore, the GCF of 77/66,154/20,129/578 is 1/190740.
To find the highest common factor of 77,154,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The factors of 129 are 1, 3, 43, 129
The HCF of 77,154,129 is 1.
Lets's calculate GCF of 77,154,129
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 77,154,129 By Matching Biggest Common Factor Method
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 77,154,129 . The biggest common factor number is the GCF number.
So the greatest common factor 77,154,129 is 1.
Lets's calculate LCM of 66,20,578
| 2 | 66, 20, 578 |
| 33, 10, 289 |
∴ So the LCM of the given numbers is 2 x 33 x 10 x 289 = 190740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/190740
Therefore, the GCF of Fractions 77/66,154/20,129/578 is 1/190740
Least Common Multiple of 66,20,578 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 66,20,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,20,578) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(66,20,578) x common factors =2 x 2 = 4
LCM(66,20,578) = ( 66 × 20 × 578 ) / 4
LCM(66,20,578) = 762960 / 4
LCM(66,20,578) = 190740
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FAQs on GCF of Fractions of 77/66, 154/20, 129/578
1. What is the HCF of 77,154,129?
The HCF of 77,154,129 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 77/66, 154/20, 129/578?
Answer: GCF of Numerators as per given numbers 77/66, 154/20, 129/578 is
GCF of Numerators i.e. for 77,154,129 is 1
LCM of denominators i.e. for 66,20,578 is 190740.
Thus, GCF of Fractions is 1/190740.Finally, GCF of Fractions for 77/66, 154/20, 129/578 is 1/190740.