GCF of 18/77, 29/86, 210/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 18/77, 29/86, 210/214 i.e 1/708554 easily. The following is the detailed procedure to determine the greatest common factor of fractions 18/77, 29/86, 210/214.
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 18/77,29/86,210/214?
Given fractions are 18/77,29/86,210/214
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 18/77,29/86,210/214, numerators are 18,29,210
Denominators are 77,86,214
The GCF of 18,29,210 is 1 .
LCM of 77,86,214 is 708554.
The greatest common factor of 18/77,29/86,210/214 = [GCF of 18,29,210]/[LCM of 77,86,214]= 1/708554
Therefore, the GCF of 18/77,29/86,210/214 is 1/708554.
To find the highest common factor of 18,29,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 29 are 1, 29
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 18,29,210 is 1.
Lets's calculate GCF of 18,29,210
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 18,29,210 By Matching Biggest Common Factor Method
Now, list down the factors of 18
:1,2,3,6,9,18
Now, list down the factors of 29
:1,29
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 18,29,210 . The biggest common factor number is the GCF number.
So the greatest common factor 18,29,210 is 1.
Lets's calculate LCM of 77,86,214
| 2 | 77, 86, 214 |
| 77, 43, 107 |
∴ So the LCM of the given numbers is 2 x 77 x 43 x 107 = 708554
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/708554
Therefore, the GCF of Fractions 18/77,29/86,210/214 is 1/708554
Least Common Multiple of 77,86,214 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 77,86,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,86,214) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(77,86,214) x common factors =1 x 2 = 2
LCM(77,86,214) = ( 77 × 86 × 214 ) / 2
LCM(77,86,214) = 1417108 / 2
LCM(77,86,214) = 708554
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FAQs on GCF of Fractions of 18/77, 29/86, 210/214
1. What is the HCF of 18,29,210?
The HCF of 18,29,210 is 1
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 18/77, 29/86, 210/214?
Answer: GCF of Numerators as per given numbers 18/77, 29/86, 210/214 is
GCF of Numerators i.e. for 18,29,210 is 1
LCM of denominators i.e. for 77,86,214 is 708554.
Thus, GCF of Fractions is 1/708554.Finally, GCF of Fractions for 18/77, 29/86, 210/214 is 1/708554.