GCF of 711/214, 1005/514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 711/214, 1005/514 i.e 3/54998 easily. The following is the detailed procedure to determine the greatest common factor of fractions 711/214, 1005/514.
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 711/214,1005/514?
Given fractions are 711/214,1005/514
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 711/214,1005/514, numerators are 711,1005
Denominators are 214,514
The GCF of 711,1005 is 3 .
LCM of 214,514 is 54998.
The greatest common factor of 711/214,1005/514 = [GCF of 711,1005]/[LCM of 214,514]= 3/54998
Therefore, the GCF of 711/214,1005/514 is 3/54998.
To find the highest common factor of 711,1005, we have to find the factors of both numbers and list the highest common factor.
The factors of 711 are 1, 3, 9, 79, 237, 711
The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005
The HCF of 711,1005 is 3.
Lets's calculate GCF of 711,1005
| 3 | 711, 1005 |
| 237, 335 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 711,1005 By Matching Biggest Common Factor Method
Now, list down the factors of 711
:1,3,9,79,237,711
Now, list down the factors of 1005
:1,3,5,15,67,201,335,1005
Greatest Common Factor
We found the factors 711,1005 . The biggest common factor number is the GCF number.
So the greatest common factor 711,1005 is 3.
Lets's calculate LCM of 214,514
| 2 | 214, 514 |
| 107, 257 |
∴ So the LCM of the given numbers is 2 x 107 x 257 = 54998
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/54998
Therefore, the GCF of Fractions 711/214,1005/514 is 3/54998
Least Common Multiple of 214,514 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 214,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,514) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,514) x common factors =2 x 1 = 2
LCM(214,514) = ( 214 × 514 ) / 2
LCM(214,514) = 109996 / 2
LCM(214,514) = 54998
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FAQs on GCF of Fractions of 711/214, 1005/514
1. What is the HCF of 711,1005?
The HCF of 711,1005 is 3
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 711/214, 1005/514?
Answer: GCF of Numerators as per given numbers 711/214, 1005/514 is
GCF of Numerators i.e. for 711,1005 is 3
LCM of denominators i.e. for 214,514 is 54998.
Thus, GCF of Fractions is 3/54998.Finally, GCF of Fractions for 711/214, 1005/514 is 3/54998.