GCF of 7298/976, 3690/7148
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7298/976, 3690/7148 i.e 82/1744112 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7298/976, 3690/7148.
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 7298/976,3690/7148?
Given fractions are 7298/976,3690/7148
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 7298/976,3690/7148, numerators are 7298,3690
Denominators are 976,7148
The GCF of 7298,3690 is 82 .
LCM of 976,7148 is 1744112.
The greatest common factor of 7298/976,3690/7148 = [GCF of 7298,3690]/[LCM of 976,7148]= 82/1744112
Therefore, the GCF of 7298/976,3690/7148 is 82/1744112.
To find the highest common factor of 7298,3690, we have to find the factors of both numbers and list the highest common factor.
The factors of 7298 are 1, 2, 41, 82, 89, 178, 3649, 7298
The factors of 3690 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 41, 45, 82, 90, 123, 205, 246, 369, 410, 615, 738, 1230, 1845, 3690
The HCF of 7298,3690 is 82.
Lets's calculate GCF of 7298,3690
| 2 | 7298, 3690 |
| 41 | 3649, 1845 |
| 89, 45 |
∴ So the GCF of the given numbers is 2 x 41 = 82
Greatest Common Factor of 7298,3690 By Matching Biggest Common Factor Method
Now, list down the factors of 7298
:1,2,41,82,89,178,3649,7298
Now, list down the factors of 3690
:1,2,3,5,6,9,10,15,18,30,41,45,82,90,123,205,246,369,410,615,738,1230,1845,3690
Greatest Common Factor
We found the factors 7298,3690 . The biggest common factor number is the GCF number.
So the greatest common factor 7298,3690 is 82.
Lets's calculate LCM of 976,7148
| 2 | 976, 7148 |
| 2 | 488, 3574 |
| 244, 1787 |
∴ So the LCM of the given numbers is 2 x 2 x 244 x 1787 = 1744112
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 82/1744112
Therefore, the GCF of Fractions 7298/976,3690/7148 is 82/1744112
Least Common Multiple of 976,7148 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 976,7148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(976,7148) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(976,7148) x common factors =4 x 1 = 4
LCM(976,7148) = ( 976 × 7148 ) / 4
LCM(976,7148) = 6976448 / 4
LCM(976,7148) = 1744112
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FAQs on GCF of Fractions of 7298/976, 3690/7148
1. What is the HCF of 7298,3690?
The HCF of 7298,3690 is 82
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 7298/976, 3690/7148?
Answer: GCF of Numerators as per given numbers 7298/976, 3690/7148 is
GCF of Numerators i.e. for 7298,3690 is 82
LCM of denominators i.e. for 976,7148 is 1744112.
Thus, GCF of Fractions is 82/1744112.Finally, GCF of Fractions for 7298/976, 3690/7148 is 82/1744112.