GCF of 66/49, 218/61, 214/61
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 66/49, 218/61, 214/61 i.e 2/2989 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/49, 218/61, 214/61.
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 66/49,218/61,214/61?
Given fractions are 66/49,218/61,214/61
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 66/49,218/61,214/61, numerators are 66,218,214
Denominators are 49,61,61
The GCF of 66,218,214 is 2 .
LCM of 49,61,61 is 2989.
The greatest common factor of 66/49,218/61,214/61 = [GCF of 66,218,214]/[LCM of 49,61,61]= 2/2989
Therefore, the GCF of 66/49,218/61,214/61 is 2/2989.
To find the highest common factor of 66,218,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 218 are 1, 2, 109, 218
The factors of 214 are 1, 2, 107, 214
The HCF of 66,218,214 is 2.
Lets's calculate GCF of 66,218,214
| 2 | 66, 218, 214 |
| 33, 109, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 66,218,214 By Matching Biggest Common Factor Method
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 218
:1,2,109,218
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 66,218,214 . The biggest common factor number is the GCF number.
So the greatest common factor 66,218,214 is 2.
Lets's calculate LCM of 49,61,61
| 61 | 49, 61, 61 |
| 49, 1, 1 |
∴ So the LCM of the given numbers is 61 x 49 x 1 x 1 = 2989
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2989
Therefore, the GCF of Fractions 66/49,218/61,214/61 is 2/2989
Least Common Multiple of 49,61,61 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 49,61,61 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,61,61) = 1
common factors(in case of two or more numbers have common factors) = 61
GCF(49,61,61) x common factors =1 x 61 = 61
LCM(49,61,61) = ( 49 × 61 × 61 ) / 61
LCM(49,61,61) = 182329 / 61
LCM(49,61,61) = 2989
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FAQs on GCF of Fractions of 66/49, 218/61, 214/61
1. What is the HCF of 66,218,214?
The HCF of 66,218,214 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 66/49, 218/61, 214/61?
Answer: GCF of Numerators as per given numbers 66/49, 218/61, 214/61 is
GCF of Numerators i.e. for 66,218,214 is 2
LCM of denominators i.e. for 49,61,61 is 2989.
Thus, GCF of Fractions is 2/2989.Finally, GCF of Fractions for 66/49, 218/61, 214/61 is 2/2989.