GCF of 82/58, 119/64, 414/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/58, 119/64, 414/218 i.e 1/202304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/58, 119/64, 414/218.
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 82/58,119/64,414/218?
Given fractions are 82/58,119/64,414/218
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 82/58,119/64,414/218, numerators are 82,119,414
Denominators are 58,64,218
The GCF of 82,119,414 is 1 .
LCM of 58,64,218 is 202304.
The greatest common factor of 82/58,119/64,414/218 = [GCF of 82,119,414]/[LCM of 58,64,218]= 1/202304
Therefore, the GCF of 82/58,119/64,414/218 is 1/202304.
To find the highest common factor of 82,119,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 119 are 1, 7, 17, 119
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 82,119,414 is 1.
Lets's calculate GCF of 82,119,414
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 82,119,414 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 119
:1,7,17,119
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 82,119,414 . The biggest common factor number is the GCF number.
So the greatest common factor 82,119,414 is 1.
Lets's calculate LCM of 58,64,218
| 2 | 58, 64, 218 |
| 29, 32, 109 |
∴ So the LCM of the given numbers is 2 x 29 x 32 x 109 = 202304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/202304
Therefore, the GCF of Fractions 82/58,119/64,414/218 is 1/202304
Least Common Multiple of 58,64,218 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 58,64,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,64,218) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(58,64,218) x common factors =2 x 2 = 4
LCM(58,64,218) = ( 58 × 64 × 218 ) / 4
LCM(58,64,218) = 809216 / 4
LCM(58,64,218) = 202304
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FAQs on GCF of Fractions of 82/58, 119/64, 414/218
1. What is the HCF of 82,119,414?
The HCF of 82,119,414 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 82/58, 119/64, 414/218?
Answer: GCF of Numerators as per given numbers 82/58, 119/64, 414/218 is
GCF of Numerators i.e. for 82,119,414 is 1
LCM of denominators i.e. for 58,64,218 is 202304.
Thus, GCF of Fractions is 1/202304.Finally, GCF of Fractions for 82/58, 119/64, 414/218 is 1/202304.