GCF of 386/512, 114/970
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 386/512, 114/970 i.e 2/248320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 386/512, 114/970.
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 386/512,114/970?
Given fractions are 386/512,114/970
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 386/512,114/970, numerators are 386,114
Denominators are 512,970
The GCF of 386,114 is 2 .
LCM of 512,970 is 248320.
The greatest common factor of 386/512,114/970 = [GCF of 386,114]/[LCM of 512,970]= 2/248320
Therefore, the GCF of 386/512,114/970 is 2/248320.
To find the highest common factor of 386,114, we have to find the factors of both numbers and list the highest common factor.
The factors of 386 are 1, 2, 193, 386
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The HCF of 386,114 is 2.
Lets's calculate GCF of 386,114
| 2 | 386, 114 |
| 193, 57 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 386,114 By Matching Biggest Common Factor Method
Now, list down the factors of 386
:1,2,193,386
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors 386,114 . The biggest common factor number is the GCF number.
So the greatest common factor 386,114 is 2.
Lets's calculate LCM of 512,970
| 2 | 512, 970 |
| 256, 485 |
∴ So the LCM of the given numbers is 2 x 256 x 485 = 248320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/248320
Therefore, the GCF of Fractions 386/512,114/970 is 2/248320
Least Common Multiple of 512,970 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 512,970 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,970) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,970) x common factors =2 x 1 = 2
LCM(512,970) = ( 512 × 970 ) / 2
LCM(512,970) = 496640 / 2
LCM(512,970) = 248320
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FAQs on GCF of Fractions of 386/512, 114/970
1. What is the HCF of 386,114?
The HCF of 386,114 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 386/512, 114/970?
Answer: GCF of Numerators as per given numbers 386/512, 114/970 is
GCF of Numerators i.e. for 386,114 is 2
LCM of denominators i.e. for 512,970 is 248320.
Thus, GCF of Fractions is 2/248320.Finally, GCF of Fractions for 386/512, 114/970 is 2/248320.