GCF of 92/49, 29/42, 219/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 92/49, 29/42, 219/686 i.e 1/2058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 92/49, 29/42, 219/686.
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 92/49,29/42,219/686?
Given fractions are 92/49,29/42,219/686
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 92/49,29/42,219/686, numerators are 92,29,219
Denominators are 49,42,686
The GCF of 92,29,219 is 1 .
LCM of 49,42,686 is 2058.
The greatest common factor of 92/49,29/42,219/686 = [GCF of 92,29,219]/[LCM of 49,42,686]= 1/2058
Therefore, the GCF of 92/49,29/42,219/686 is 1/2058.
To find the highest common factor of 92,29,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 92 are 1, 2, 4, 23, 46, 92
The factors of 29 are 1, 29
The factors of 219 are 1, 3, 73, 219
The HCF of 92,29,219 is 1.
Lets's calculate GCF of 92,29,219
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 92,29,219 By Matching Biggest Common Factor Method
Now, list down the factors of 92
:1,2,4,23,46,92
Now, list down the factors of 29
:1,29
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 92,29,219 . The biggest common factor number is the GCF number.
So the greatest common factor 92,29,219 is 1.
Lets's calculate LCM of 49,42,686
| 2 | 49, 42, 686 |
| 7 | 49, 21, 343 |
| 7 | 7, 3, 49 |
| 1, 3, 7 |
∴ So the LCM of the given numbers is 2 x 7 x 7 x 1 x 3 x 7 = 2058
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2058
Therefore, the GCF of Fractions 92/49,29/42,219/686 is 1/2058
Least Common Multiple of 49,42,686 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 49,42,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,42,686) = 7
common factors(in case of two or more numbers have common factors) = 98
GCF(49,42,686) x common factors =7 x 98 = 686
LCM(49,42,686) = ( 49 × 42 × 686 ) / 686
LCM(49,42,686) = 1411788 / 686
LCM(49,42,686) = 2058
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FAQs on GCF of Fractions of 92/49, 29/42, 219/686
1. What is the HCF of 92,29,219?
The HCF of 92,29,219 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 92/49, 29/42, 219/686?
Answer: GCF of Numerators as per given numbers 92/49, 29/42, 219/686 is
GCF of Numerators i.e. for 92,29,219 is 1
LCM of denominators i.e. for 49,42,686 is 2058.
Thus, GCF of Fractions is 1/2058.Finally, GCF of Fractions for 92/49, 29/42, 219/686 is 1/2058.