GCF of 514/215, 214/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 514/215, 214/106 i.e 2/22790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/215, 214/106.
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 514/215,214/106?
Given fractions are 514/215,214/106
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 514/215,214/106, numerators are 514,214
Denominators are 215,106
The GCF of 514,214 is 2 .
LCM of 215,106 is 22790.
The greatest common factor of 514/215,214/106 = [GCF of 514,214]/[LCM of 215,106]= 2/22790
Therefore, the GCF of 514/215,214/106 is 2/22790.
To find the highest common factor of 514,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 214 are 1, 2, 107, 214
The HCF of 514,214 is 2.
Lets's calculate GCF of 514,214
| 2 | 514, 214 |
| 257, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 514,214 By Matching Biggest Common Factor Method
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 514,214 . The biggest common factor number is the GCF number.
So the greatest common factor 514,214 is 2.
Lets's calculate LCM of 215,106
Given numbers has no common factors except 1. So, there LCM is their product i.e 22790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/22790
Therefore, the GCF of Fractions 514/215,214/106 is 2/22790
Least Common Multiple of 215,106 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 215,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(215,106) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(215,106) x common factors =1 x 1 = 1
LCM(215,106) = ( 215 × 106 ) / 1
LCM(215,106) = 22790 / 1
LCM(215,106) = 22790
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FAQs on GCF of Fractions of 514/215, 214/106
1. What is the HCF of 514,214?
The HCF of 514,214 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 514/215, 214/106?
Answer: GCF of Numerators as per given numbers 514/215, 214/106 is
GCF of Numerators i.e. for 514,214 is 2
LCM of denominators i.e. for 215,106 is 22790.
Thus, GCF of Fractions is 2/22790.Finally, GCF of Fractions for 514/215, 214/106 is 2/22790.