GCF of 4123/802, 7742/4342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4123/802, 7742/4342 i.e 7/1741142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4123/802, 7742/4342.
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 4123/802,7742/4342?
Given fractions are 4123/802,7742/4342
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 4123/802,7742/4342, numerators are 4123,7742
Denominators are 802,4342
The GCF of 4123,7742 is 7 .
LCM of 802,4342 is 1741142.
The greatest common factor of 4123/802,7742/4342 = [GCF of 4123,7742]/[LCM of 802,4342]= 7/1741142
Therefore, the GCF of 4123/802,7742/4342 is 7/1741142.
To find the highest common factor of 4123,7742, we have to find the factors of both numbers and list the highest common factor.
The factors of 4123 are 1, 7, 19, 31, 133, 217, 589, 4123
The factors of 7742 are 1, 2, 7, 14, 49, 79, 98, 158, 553, 1106, 3871, 7742
The HCF of 4123,7742 is 7.
Lets's calculate GCF of 4123,7742
| 7 | 4123, 7742 |
| 589, 1106 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 4123,7742 By Matching Biggest Common Factor Method
Now, list down the factors of 4123
:1,7,19,31,133,217,589,4123
Now, list down the factors of 7742
:1,2,7,14,49,79,98,158,553,1106,3871,7742
Greatest Common Factor
We found the factors 4123,7742 . The biggest common factor number is the GCF number.
So the greatest common factor 4123,7742 is 7.
Lets's calculate LCM of 802,4342
| 2 | 802, 4342 |
| 401, 2171 |
∴ So the LCM of the given numbers is 2 x 401 x 2171 = 1741142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/1741142
Therefore, the GCF of Fractions 4123/802,7742/4342 is 7/1741142
Least Common Multiple of 802,4342 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 802,4342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(802,4342) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(802,4342) x common factors =2 x 1 = 2
LCM(802,4342) = ( 802 × 4342 ) / 2
LCM(802,4342) = 3482284 / 2
LCM(802,4342) = 1741142
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FAQs on GCF of Fractions of 4123/802, 7742/4342
1. What is the HCF of 4123,7742?
The HCF of 4123,7742 is 7
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 4123/802, 7742/4342?
Answer: GCF of Numerators as per given numbers 4123/802, 7742/4342 is
GCF of Numerators i.e. for 4123,7742 is 7
LCM of denominators i.e. for 802,4342 is 1741142.
Thus, GCF of Fractions is 7/1741142.Finally, GCF of Fractions for 4123/802, 7742/4342 is 7/1741142.