GCF of 998/694, 5814/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 998/694, 5814/209 i.e 2/145046 easily. The following is the detailed procedure to determine the greatest common factor of fractions 998/694, 5814/209.
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 998/694,5814/209?
Given fractions are 998/694,5814/209
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 998/694,5814/209, numerators are 998,5814
Denominators are 694,209
The GCF of 998,5814 is 2 .
LCM of 694,209 is 145046.
The greatest common factor of 998/694,5814/209 = [GCF of 998,5814]/[LCM of 694,209]= 2/145046
Therefore, the GCF of 998/694,5814/209 is 2/145046.
To find the highest common factor of 998,5814, we have to find the factors of both numbers and list the highest common factor.
The factors of 998 are 1, 2, 499, 998
The factors of 5814 are 1, 2, 3, 6, 9, 17, 18, 19, 34, 38, 51, 57, 102, 114, 153, 171, 306, 323, 342, 646, 969, 1938, 2907, 5814
The HCF of 998,5814 is 2.
Lets's calculate GCF of 998,5814
| 2 | 998, 5814 |
| 499, 2907 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 998,5814 By Matching Biggest Common Factor Method
Now, list down the factors of 998
:1,2,499,998
Now, list down the factors of 5814
:1,2,3,6,9,17,18,19,34,38,51,57,102,114,153,171,306,323,342,646,969,1938,2907,5814
Greatest Common Factor
We found the factors 998,5814 . The biggest common factor number is the GCF number.
So the greatest common factor 998,5814 is 2.
Lets's calculate LCM of 694,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 145046
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/145046
Therefore, the GCF of Fractions 998/694,5814/209 is 2/145046
Least Common Multiple of 694,209 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 694,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(694,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(694,209) x common factors =1 x 1 = 1
LCM(694,209) = ( 694 × 209 ) / 1
LCM(694,209) = 145046 / 1
LCM(694,209) = 145046
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FAQs on GCF of Fractions of 998/694, 5814/209
1. What is the HCF of 998,5814?
The HCF of 998,5814 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 998/694, 5814/209?
Answer: GCF of Numerators as per given numbers 998/694, 5814/209 is
GCF of Numerators i.e. for 998,5814 is 2
LCM of denominators i.e. for 694,209 is 145046.
Thus, GCF of Fractions is 2/145046.Finally, GCF of Fractions for 998/694, 5814/209 is 2/145046.