GCF of 8290/823, 7658/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8290/823, 7658/414 i.e 2/340722 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8290/823, 7658/414.
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 8290/823,7658/414?
Given fractions are 8290/823,7658/414
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 8290/823,7658/414, numerators are 8290,7658
Denominators are 823,414
The GCF of 8290,7658 is 2 .
LCM of 823,414 is 340722.
The greatest common factor of 8290/823,7658/414 = [GCF of 8290,7658]/[LCM of 823,414]= 2/340722
Therefore, the GCF of 8290/823,7658/414 is 2/340722.
To find the highest common factor of 8290,7658, we have to find the factors of both numbers and list the highest common factor.
The factors of 8290 are 1, 2, 5, 10, 829, 1658, 4145, 8290
The factors of 7658 are 1, 2, 7, 14, 547, 1094, 3829, 7658
The HCF of 8290,7658 is 2.
Lets's calculate GCF of 8290,7658
| 2 | 8290, 7658 |
| 4145, 3829 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8290,7658 By Matching Biggest Common Factor Method
Now, list down the factors of 8290
:1,2,5,10,829,1658,4145,8290
Now, list down the factors of 7658
:1,2,7,14,547,1094,3829,7658
Greatest Common Factor
We found the factors 8290,7658 . The biggest common factor number is the GCF number.
So the greatest common factor 8290,7658 is 2.
Lets's calculate LCM of 823,414
Given numbers has no common factors except 1. So, there LCM is their product i.e 340722
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/340722
Therefore, the GCF of Fractions 8290/823,7658/414 is 2/340722
Least Common Multiple of 823,414 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 823,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(823,414) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(823,414) x common factors =1 x 1 = 1
LCM(823,414) = ( 823 × 414 ) / 1
LCM(823,414) = 340722 / 1
LCM(823,414) = 340722
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FAQs on GCF of Fractions of 8290/823, 7658/414
1. What is the HCF of 8290,7658?
The HCF of 8290,7658 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 8290/823, 7658/414?
Answer: GCF of Numerators as per given numbers 8290/823, 7658/414 is
GCF of Numerators i.e. for 8290,7658 is 2
LCM of denominators i.e. for 823,414 is 340722.
Thus, GCF of Fractions is 2/340722.Finally, GCF of Fractions for 8290/823, 7658/414 is 2/340722.