GCF of 682/219, 174/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 682/219, 174/214 i.e 2/46866 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/219, 174/214.
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 682/219,174/214?
Given fractions are 682/219,174/214
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 682/219,174/214, numerators are 682,174
Denominators are 219,214
The GCF of 682,174 is 2 .
LCM of 219,214 is 46866.
The greatest common factor of 682/219,174/214 = [GCF of 682,174]/[LCM of 219,214]= 2/46866
Therefore, the GCF of 682/219,174/214 is 2/46866.
To find the highest common factor of 682,174, we have to find the factors of both numbers and list the highest common factor.
The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174
The HCF of 682,174 is 2.
Lets's calculate GCF of 682,174
| 2 | 682, 174 |
| 341, 87 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 682,174 By Matching Biggest Common Factor Method
Now, list down the factors of 682
:1,2,11,22,31,62,341,682
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Greatest Common Factor
We found the factors 682,174 . The biggest common factor number is the GCF number.
So the greatest common factor 682,174 is 2.
Lets's calculate LCM of 219,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 46866
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/46866
Therefore, the GCF of Fractions 682/219,174/214 is 2/46866
Least Common Multiple of 219,214 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 219,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(219,214) x common factors =1 x 1 = 1
LCM(219,214) = ( 219 × 214 ) / 1
LCM(219,214) = 46866 / 1
LCM(219,214) = 46866
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FAQs on GCF of Fractions of 682/219, 174/214
1. What is the HCF of 682,174?
The HCF of 682,174 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 682/219, 174/214?
Answer: GCF of Numerators as per given numbers 682/219, 174/214 is
GCF of Numerators i.e. for 682,174 is 2
LCM of denominators i.e. for 219,214 is 46866.
Thus, GCF of Fractions is 2/46866.Finally, GCF of Fractions for 682/219, 174/214 is 2/46866.