GCF of 7539/378, 5514/8343
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7539/378, 5514/8343 i.e 3/116802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7539/378, 5514/8343.
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 7539/378,5514/8343?
Given fractions are 7539/378,5514/8343
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 7539/378,5514/8343, numerators are 7539,5514
Denominators are 378,8343
The GCF of 7539,5514 is 3 .
LCM of 378,8343 is 116802.
The greatest common factor of 7539/378,5514/8343 = [GCF of 7539,5514]/[LCM of 378,8343]= 3/116802
Therefore, the GCF of 7539/378,5514/8343 is 3/116802.
To find the highest common factor of 7539,5514, we have to find the factors of both numbers and list the highest common factor.
The factors of 7539 are 1, 3, 7, 21, 359, 1077, 2513, 7539
The factors of 5514 are 1, 2, 3, 6, 919, 1838, 2757, 5514
The HCF of 7539,5514 is 3.
Lets's calculate GCF of 7539,5514
| 3 | 7539, 5514 |
| 2513, 1838 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7539,5514 By Matching Biggest Common Factor Method
Now, list down the factors of 7539
:1,3,7,21,359,1077,2513,7539
Now, list down the factors of 5514
:1,2,3,6,919,1838,2757,5514
Greatest Common Factor
We found the factors 7539,5514 . The biggest common factor number is the GCF number.
So the greatest common factor 7539,5514 is 3.
Lets's calculate LCM of 378,8343
| 3 | 378, 8343 |
| 3 | 126, 2781 |
| 3 | 42, 927 |
| 14, 309 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 14 x 309 = 116802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/116802
Therefore, the GCF of Fractions 7539/378,5514/8343 is 3/116802
Least Common Multiple of 378,8343 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 378,8343 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,8343) = 27
common factors(in case of two or more numbers have common factors) = 1
GCF(378,8343) x common factors =27 x 1 = 27
LCM(378,8343) = ( 378 × 8343 ) / 27
LCM(378,8343) = 3153654 / 27
LCM(378,8343) = 116802
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FAQs on GCF of Fractions of 7539/378, 5514/8343
1. What is the HCF of 7539,5514?
The HCF of 7539,5514 is 3
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 7539/378, 5514/8343?
Answer: GCF of Numerators as per given numbers 7539/378, 5514/8343 is
GCF of Numerators i.e. for 7539,5514 is 3
LCM of denominators i.e. for 378,8343 is 116802.
Thus, GCF of Fractions is 3/116802.Finally, GCF of Fractions for 7539/378, 5514/8343 is 3/116802.