GCF of 760/82, 342/2178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 760/82, 342/2178 i.e 38/89298 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/82, 342/2178.
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 760/82,342/2178?
Given fractions are 760/82,342/2178
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 760/82,342/2178, numerators are 760,342
Denominators are 82,2178
The GCF of 760,342 is 38 .
LCM of 82,2178 is 89298.
The greatest common factor of 760/82,342/2178 = [GCF of 760,342]/[LCM of 82,2178]= 38/89298
Therefore, the GCF of 760/82,342/2178 is 38/89298.
To find the highest common factor of 760,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 760,342 is 38.
Lets's calculate GCF of 760,342
| 2 | 760, 342 |
| 19 | 380, 171 |
| 20, 9 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 760,342 By Matching Biggest Common Factor Method
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 760,342 . The biggest common factor number is the GCF number.
So the greatest common factor 760,342 is 38.
Lets's calculate LCM of 82,2178
| 2 | 82, 2178 |
| 41, 1089 |
∴ So the LCM of the given numbers is 2 x 41 x 1089 = 89298
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/89298
Therefore, the GCF of Fractions 760/82,342/2178 is 38/89298
Least Common Multiple of 82,2178 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 82,2178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,2178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,2178) x common factors =2 x 1 = 2
LCM(82,2178) = ( 82 × 2178 ) / 2
LCM(82,2178) = 178596 / 2
LCM(82,2178) = 89298
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FAQs on GCF of Fractions of 760/82, 342/2178
1. What is the HCF of 760,342?
The HCF of 760,342 is 38
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 760/82, 342/2178?
Answer: GCF of Numerators as per given numbers 760/82, 342/2178 is
GCF of Numerators i.e. for 760,342 is 38
LCM of denominators i.e. for 82,2178 is 89298.
Thus, GCF of Fractions is 38/89298.Finally, GCF of Fractions for 760/82, 342/2178 is 38/89298.