GCF of 5474/822, 9926/164
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5474/822, 9926/164 i.e 14/67404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5474/822, 9926/164.
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 5474/822,9926/164?
Given fractions are 5474/822,9926/164
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 5474/822,9926/164, numerators are 5474,9926
Denominators are 822,164
The GCF of 5474,9926 is 14 .
LCM of 822,164 is 67404.
The greatest common factor of 5474/822,9926/164 = [GCF of 5474,9926]/[LCM of 822,164]= 14/67404
Therefore, the GCF of 5474/822,9926/164 is 14/67404.
To find the highest common factor of 5474,9926, we have to find the factors of both numbers and list the highest common factor.
The factors of 5474 are 1, 2, 7, 14, 17, 23, 34, 46, 119, 161, 238, 322, 391, 782, 2737, 5474
The factors of 9926 are 1, 2, 7, 14, 709, 1418, 4963, 9926
The HCF of 5474,9926 is 14.
Lets's calculate GCF of 5474,9926
| 2 | 5474, 9926 |
| 7 | 2737, 4963 |
| 391, 709 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 5474,9926 By Matching Biggest Common Factor Method
Now, list down the factors of 5474
:1,2,7,14,17,23,34,46,119,161,238,322,391,782,2737,5474
Now, list down the factors of 9926
:1,2,7,14,709,1418,4963,9926
Greatest Common Factor
We found the factors 5474,9926 . The biggest common factor number is the GCF number.
So the greatest common factor 5474,9926 is 14.
Lets's calculate LCM of 822,164
| 2 | 822, 164 |
| 411, 82 |
∴ So the LCM of the given numbers is 2 x 411 x 82 = 67404
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/67404
Therefore, the GCF of Fractions 5474/822,9926/164 is 14/67404
Least Common Multiple of 822,164 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 822,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(822,164) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(822,164) x common factors =2 x 1 = 2
LCM(822,164) = ( 822 × 164 ) / 2
LCM(822,164) = 134808 / 2
LCM(822,164) = 67404
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FAQs on GCF of Fractions of 5474/822, 9926/164
1. What is the HCF of 5474,9926?
The HCF of 5474,9926 is 14
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 5474/822, 9926/164?
Answer: GCF of Numerators as per given numbers 5474/822, 9926/164 is
GCF of Numerators i.e. for 5474,9926 is 14
LCM of denominators i.e. for 822,164 is 67404.
Thus, GCF of Fractions is 14/67404.Finally, GCF of Fractions for 5474/822, 9926/164 is 14/67404.