GCF of 2106/814, 7690/1968
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2106/814, 7690/1968 i.e 2/800976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2106/814, 7690/1968.
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 2106/814,7690/1968?
Given fractions are 2106/814,7690/1968
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 2106/814,7690/1968, numerators are 2106,7690
Denominators are 814,1968
The GCF of 2106,7690 is 2 .
LCM of 814,1968 is 800976.
The greatest common factor of 2106/814,7690/1968 = [GCF of 2106,7690]/[LCM of 814,1968]= 2/800976
Therefore, the GCF of 2106/814,7690/1968 is 2/800976.
To find the highest common factor of 2106,7690, we have to find the factors of both numbers and list the highest common factor.
The factors of 2106 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106
The factors of 7690 are 1, 2, 5, 10, 769, 1538, 3845, 7690
The HCF of 2106,7690 is 2.
Lets's calculate GCF of 2106,7690
| 2 | 2106, 7690 |
| 1053, 3845 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2106,7690 By Matching Biggest Common Factor Method
Now, list down the factors of 2106
:1,2,3,6,9,13,18,26,27,39,54,78,81,117,162,234,351,702,1053,2106
Now, list down the factors of 7690
:1,2,5,10,769,1538,3845,7690
Greatest Common Factor
We found the factors 2106,7690 . The biggest common factor number is the GCF number.
So the greatest common factor 2106,7690 is 2.
Lets's calculate LCM of 814,1968
| 2 | 814, 1968 |
| 407, 984 |
∴ So the LCM of the given numbers is 2 x 407 x 984 = 800976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/800976
Therefore, the GCF of Fractions 2106/814,7690/1968 is 2/800976
Least Common Multiple of 814,1968 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 814,1968 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,1968) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(814,1968) x common factors =2 x 1 = 2
LCM(814,1968) = ( 814 × 1968 ) / 2
LCM(814,1968) = 1601952 / 2
LCM(814,1968) = 800976
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FAQs on GCF of Fractions of 2106/814, 7690/1968
1. What is the HCF of 2106,7690?
The HCF of 2106,7690 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 2106/814, 7690/1968?
Answer: GCF of Numerators as per given numbers 2106/814, 7690/1968 is
GCF of Numerators i.e. for 2106,7690 is 2
LCM of denominators i.e. for 814,1968 is 800976.
Thus, GCF of Fractions is 2/800976.Finally, GCF of Fractions for 2106/814, 7690/1968 is 2/800976.