GCF of 554/311, 414/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 554/311, 414/218 i.e 2/67798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 554/311, 414/218.
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 554/311,414/218?
Given fractions are 554/311,414/218
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 554/311,414/218, numerators are 554,414
Denominators are 311,218
The GCF of 554,414 is 2 .
LCM of 311,218 is 67798.
The greatest common factor of 554/311,414/218 = [GCF of 554,414]/[LCM of 311,218]= 2/67798
Therefore, the GCF of 554/311,414/218 is 2/67798.
To find the highest common factor of 554,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 554 are 1, 2, 277, 554
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 554,414 is 2.
Lets's calculate GCF of 554,414
| 2 | 554, 414 |
| 277, 207 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 554,414 By Matching Biggest Common Factor Method
Now, list down the factors of 554
:1,2,277,554
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 554,414 . The biggest common factor number is the GCF number.
So the greatest common factor 554,414 is 2.
Lets's calculate LCM of 311,218
Given numbers has no common factors except 1. So, there LCM is their product i.e 67798
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/67798
Therefore, the GCF of Fractions 554/311,414/218 is 2/67798
Least Common Multiple of 311,218 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 311,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(311,218) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(311,218) x common factors =1 x 1 = 1
LCM(311,218) = ( 311 × 218 ) / 1
LCM(311,218) = 67798 / 1
LCM(311,218) = 67798
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FAQs on GCF of Fractions of 554/311, 414/218
1. What is the HCF of 554,414?
The HCF of 554,414 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 554/311, 414/218?
Answer: GCF of Numerators as per given numbers 554/311, 414/218 is
GCF of Numerators i.e. for 554,414 is 2
LCM of denominators i.e. for 311,218 is 67798.
Thus, GCF of Fractions is 2/67798.Finally, GCF of Fractions for 554/311, 414/218 is 2/67798.