GCF of 2704/814, 1722/9889
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2704/814, 1722/9889 i.e 2/731786 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2704/814, 1722/9889.
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 2704/814,1722/9889?
Given fractions are 2704/814,1722/9889
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 2704/814,1722/9889, numerators are 2704,1722
Denominators are 814,9889
The GCF of 2704,1722 is 2 .
LCM of 814,9889 is 731786.
The greatest common factor of 2704/814,1722/9889 = [GCF of 2704,1722]/[LCM of 814,9889]= 2/731786
Therefore, the GCF of 2704/814,1722/9889 is 2/731786.
To find the highest common factor of 2704,1722, we have to find the factors of both numbers and list the highest common factor.
The factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704
The factors of 1722 are 1, 2, 3, 6, 7, 14, 21, 41, 42, 82, 123, 246, 287, 574, 861, 1722
The HCF of 2704,1722 is 2.
Lets's calculate GCF of 2704,1722
| 2 | 2704, 1722 |
| 1352, 861 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2704,1722 By Matching Biggest Common Factor Method
Now, list down the factors of 2704
:1,2,4,8,13,16,26,52,104,169,208,338,676,1352,2704
Now, list down the factors of 1722
:1,2,3,6,7,14,21,41,42,82,123,246,287,574,861,1722
Greatest Common Factor
We found the factors 2704,1722 . The biggest common factor number is the GCF number.
So the greatest common factor 2704,1722 is 2.
Lets's calculate LCM of 814,9889
| 11 | 814, 9889 |
| 74, 899 |
∴ So the LCM of the given numbers is 11 x 74 x 899 = 731786
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/731786
Therefore, the GCF of Fractions 2704/814,1722/9889 is 2/731786
Least Common Multiple of 814,9889 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 814,9889 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,9889) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(814,9889) x common factors =11 x 1 = 11
LCM(814,9889) = ( 814 × 9889 ) / 11
LCM(814,9889) = 8049646 / 11
LCM(814,9889) = 731786
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FAQs on GCF of Fractions of 2704/814, 1722/9889
1. What is the HCF of 2704,1722?
The HCF of 2704,1722 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 2704/814, 1722/9889?
Answer: GCF of Numerators as per given numbers 2704/814, 1722/9889 is
GCF of Numerators i.e. for 2704,1722 is 2
LCM of denominators i.e. for 814,9889 is 731786.
Thus, GCF of Fractions is 2/731786.Finally, GCF of Fractions for 2704/814, 1722/9889 is 2/731786.