GCF of 6854/706, 1704/1030
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6854/706, 1704/1030 i.e 2/363590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6854/706, 1704/1030.
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 6854/706,1704/1030?
Given fractions are 6854/706,1704/1030
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 6854/706,1704/1030, numerators are 6854,1704
Denominators are 706,1030
The GCF of 6854,1704 is 2 .
LCM of 706,1030 is 363590.
The greatest common factor of 6854/706,1704/1030 = [GCF of 6854,1704]/[LCM of 706,1030]= 2/363590
Therefore, the GCF of 6854/706,1704/1030 is 2/363590.
To find the highest common factor of 6854,1704, we have to find the factors of both numbers and list the highest common factor.
The factors of 6854 are 1, 2, 23, 46, 149, 298, 3427, 6854
The factors of 1704 are 1, 2, 3, 4, 6, 8, 12, 24, 71, 142, 213, 284, 426, 568, 852, 1704
The HCF of 6854,1704 is 2.
Lets's calculate GCF of 6854,1704
| 2 | 6854, 1704 |
| 3427, 852 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6854,1704 By Matching Biggest Common Factor Method
Now, list down the factors of 6854
:1,2,23,46,149,298,3427,6854
Now, list down the factors of 1704
:1,2,3,4,6,8,12,24,71,142,213,284,426,568,852,1704
Greatest Common Factor
We found the factors 6854,1704 . The biggest common factor number is the GCF number.
So the greatest common factor 6854,1704 is 2.
Lets's calculate LCM of 706,1030
| 2 | 706, 1030 |
| 353, 515 |
∴ So the LCM of the given numbers is 2 x 353 x 515 = 363590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/363590
Therefore, the GCF of Fractions 6854/706,1704/1030 is 2/363590
Least Common Multiple of 706,1030 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 706,1030 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,1030) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(706,1030) x common factors =2 x 1 = 2
LCM(706,1030) = ( 706 × 1030 ) / 2
LCM(706,1030) = 727180 / 2
LCM(706,1030) = 363590
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FAQs on GCF of Fractions of 6854/706, 1704/1030
1. What is the HCF of 6854,1704?
The HCF of 6854,1704 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 6854/706, 1704/1030?
Answer: GCF of Numerators as per given numbers 6854/706, 1704/1030 is
GCF of Numerators i.e. for 6854,1704 is 2
LCM of denominators i.e. for 706,1030 is 363590.
Thus, GCF of Fractions is 2/363590.Finally, GCF of Fractions for 6854/706, 1704/1030 is 2/363590.