GCF of 861/438, 8694/7686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 861/438, 8694/7686 i.e 21/561078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 861/438, 8694/7686.
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 861/438,8694/7686?
Given fractions are 861/438,8694/7686
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 861/438,8694/7686, numerators are 861,8694
Denominators are 438,7686
The GCF of 861,8694 is 21 .
LCM of 438,7686 is 561078.
The greatest common factor of 861/438,8694/7686 = [GCF of 861,8694]/[LCM of 438,7686]= 21/561078
Therefore, the GCF of 861/438,8694/7686 is 21/561078.
To find the highest common factor of 861,8694, we have to find the factors of both numbers and list the highest common factor.
The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861
The factors of 8694 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 23, 27, 42, 46, 54, 63, 69, 126, 138, 161, 189, 207, 322, 378, 414, 483, 621, 966, 1242, 1449, 2898, 4347, 8694
The HCF of 861,8694 is 21.
Lets's calculate GCF of 861,8694
| 3 | 861, 8694 |
| 7 | 287, 2898 |
| 41, 414 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 861,8694 By Matching Biggest Common Factor Method
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Now, list down the factors of 8694
:1,2,3,6,7,9,14,18,21,23,27,42,46,54,63,69,126,138,161,189,207,322,378,414,483,621,966,1242,1449,2898,4347,8694
Greatest Common Factor
We found the factors 861,8694 . The biggest common factor number is the GCF number.
So the greatest common factor 861,8694 is 21.
Lets's calculate LCM of 438,7686
| 2 | 438, 7686 |
| 3 | 219, 3843 |
| 73, 1281 |
∴ So the LCM of the given numbers is 2 x 3 x 73 x 1281 = 561078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/561078
Therefore, the GCF of Fractions 861/438,8694/7686 is 21/561078
Least Common Multiple of 438,7686 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 438,7686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(438,7686) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(438,7686) x common factors =6 x 1 = 6
LCM(438,7686) = ( 438 × 7686 ) / 6
LCM(438,7686) = 3366468 / 6
LCM(438,7686) = 561078
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FAQs on GCF of Fractions of 861/438, 8694/7686
1. What is the HCF of 861,8694?
The HCF of 861,8694 is 21
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 861/438, 8694/7686?
Answer: GCF of Numerators as per given numbers 861/438, 8694/7686 is
GCF of Numerators i.e. for 861,8694 is 21
LCM of denominators i.e. for 438,7686 is 561078.
Thus, GCF of Fractions is 21/561078.Finally, GCF of Fractions for 861/438, 8694/7686 is 21/561078.