GCF of 410/109, 9726/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 410/109, 9726/678 i.e 2/73902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/109, 9726/678.
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 410/109,9726/678?
Given fractions are 410/109,9726/678
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 410/109,9726/678, numerators are 410,9726
Denominators are 109,678
The GCF of 410,9726 is 2 .
LCM of 109,678 is 73902.
The greatest common factor of 410/109,9726/678 = [GCF of 410,9726]/[LCM of 109,678]= 2/73902
Therefore, the GCF of 410/109,9726/678 is 2/73902.
To find the highest common factor of 410,9726, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 9726 are 1, 2, 3, 6, 1621, 3242, 4863, 9726
The HCF of 410,9726 is 2.
Lets's calculate GCF of 410,9726
| 2 | 410, 9726 |
| 205, 4863 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 410,9726 By Matching Biggest Common Factor Method
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 9726
:1,2,3,6,1621,3242,4863,9726
Greatest Common Factor
We found the factors 410,9726 . The biggest common factor number is the GCF number.
So the greatest common factor 410,9726 is 2.
Lets's calculate LCM of 109,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 73902
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/73902
Therefore, the GCF of Fractions 410/109,9726/678 is 2/73902
Least Common Multiple of 109,678 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 109,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(109,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(109,678) x common factors =1 x 1 = 1
LCM(109,678) = ( 109 × 678 ) / 1
LCM(109,678) = 73902 / 1
LCM(109,678) = 73902
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FAQs on GCF of Fractions of 410/109, 9726/678
1. What is the HCF of 410,9726?
The HCF of 410,9726 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 410/109, 9726/678?
Answer: GCF of Numerators as per given numbers 410/109, 9726/678 is
GCF of Numerators i.e. for 410,9726 is 2
LCM of denominators i.e. for 109,678 is 73902.
Thus, GCF of Fractions is 2/73902.Finally, GCF of Fractions for 410/109, 9726/678 is 2/73902.