GCF of 546/270, 434/212
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 546/270, 434/212 i.e 14/28620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/270, 434/212.
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 546/270,434/212?
Given fractions are 546/270,434/212
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 546/270,434/212, numerators are 546,434
Denominators are 270,212
The GCF of 546,434 is 14 .
LCM of 270,212 is 28620.
The greatest common factor of 546/270,434/212 = [GCF of 546,434]/[LCM of 270,212]= 14/28620
Therefore, the GCF of 546/270,434/212 is 14/28620.
To find the highest common factor of 546,434, we have to find the factors of both numbers and list the highest common factor.
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434
The HCF of 546,434 is 14.
Lets's calculate GCF of 546,434
| 2 | 546, 434 |
| 7 | 273, 217 |
| 39, 31 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 546,434 By Matching Biggest Common Factor Method
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Now, list down the factors of 434
:1,2,7,14,31,62,217,434
Greatest Common Factor
We found the factors 546,434 . The biggest common factor number is the GCF number.
So the greatest common factor 546,434 is 14.
Lets's calculate LCM of 270,212
| 2 | 270, 212 |
| 135, 106 |
∴ So the LCM of the given numbers is 2 x 135 x 106 = 28620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/28620
Therefore, the GCF of Fractions 546/270,434/212 is 14/28620
Least Common Multiple of 270,212 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 270,212 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,212) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(270,212) x common factors =2 x 1 = 2
LCM(270,212) = ( 270 × 212 ) / 2
LCM(270,212) = 57240 / 2
LCM(270,212) = 28620
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FAQs on GCF of Fractions of 546/270, 434/212
1. What is the HCF of 546,434?
The HCF of 546,434 is 14
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 546/270, 434/212?
Answer: GCF of Numerators as per given numbers 546/270, 434/212 is
GCF of Numerators i.e. for 546,434 is 14
LCM of denominators i.e. for 270,212 is 28620.
Thus, GCF of Fractions is 14/28620.Finally, GCF of Fractions for 546/270, 434/212 is 14/28620.