GCF of 204/98, 357/66, 119/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 204/98, 357/66, 119/78 i.e 17/42042 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/98, 357/66, 119/78.
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 204/98,357/66,119/78?
Given fractions are 204/98,357/66,119/78
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 204/98,357/66,119/78, numerators are 204,357,119
Denominators are 98,66,78
The GCF of 204,357,119 is 17 .
LCM of 98,66,78 is 42042.
The greatest common factor of 204/98,357/66,119/78 = [GCF of 204,357,119]/[LCM of 98,66,78]= 17/42042
Therefore, the GCF of 204/98,357/66,119/78 is 17/42042.
To find the highest common factor of 204,357,119, we have to find the factors of both numbers and list the highest common factor.
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357
The factors of 119 are 1, 7, 17, 119
The HCF of 204,357,119 is 17.
Lets's calculate GCF of 204,357,119
| 17 | 204, 357, 119 |
| 12, 21, 7 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 204,357,119 By Matching Biggest Common Factor Method
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Now, list down the factors of 357
:1,3,7,17,21,51,119,357
Now, list down the factors of 119
:1,7,17,119
Greatest Common Factor
We found the factors 204,357,119 . The biggest common factor number is the GCF number.
So the greatest common factor 204,357,119 is 17.
Lets's calculate LCM of 98,66,78
| 2 | 98, 66, 78 |
| 3 | 49, 33, 39 |
| 49, 11, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 49 x 11 x 13 = 42042
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/42042
Therefore, the GCF of Fractions 204/98,357/66,119/78 is 17/42042
Least Common Multiple of 98,66,78 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 98,66,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(98,66,78) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(98,66,78) x common factors =2 x 6 = 12
LCM(98,66,78) = ( 98 × 66 × 78 ) / 12
LCM(98,66,78) = 504504 / 12
LCM(98,66,78) = 42042
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FAQs on GCF of Fractions of 204/98, 357/66, 119/78
1. What is the HCF of 204,357,119?
The HCF of 204,357,119 is 17
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 204/98, 357/66, 119/78?
Answer: GCF of Numerators as per given numbers 204/98, 357/66, 119/78 is
GCF of Numerators i.e. for 204,357,119 is 17
LCM of denominators i.e. for 98,66,78 is 42042.
Thus, GCF of Fractions is 17/42042.Finally, GCF of Fractions for 204/98, 357/66, 119/78 is 17/42042.