GCF of 7191/686, 6783/8538
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7191/686, 6783/8538 i.e 51/2928534 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7191/686, 6783/8538.
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 7191/686,6783/8538?
Given fractions are 7191/686,6783/8538
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 7191/686,6783/8538, numerators are 7191,6783
Denominators are 686,8538
The GCF of 7191,6783 is 51 .
LCM of 686,8538 is 2928534.
The greatest common factor of 7191/686,6783/8538 = [GCF of 7191,6783]/[LCM of 686,8538]= 51/2928534
Therefore, the GCF of 7191/686,6783/8538 is 51/2928534.
To find the highest common factor of 7191,6783, we have to find the factors of both numbers and list the highest common factor.
The factors of 7191 are 1, 3, 9, 17, 47, 51, 141, 153, 423, 799, 2397, 7191
The factors of 6783 are 1, 3, 7, 17, 19, 21, 51, 57, 119, 133, 323, 357, 399, 969, 2261, 6783
The HCF of 7191,6783 is 51.
Lets's calculate GCF of 7191,6783
| 3 | 7191, 6783 |
| 17 | 2397, 2261 |
| 141, 133 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Greatest Common Factor of 7191,6783 By Matching Biggest Common Factor Method
Now, list down the factors of 7191
:1,3,9,17,47,51,141,153,423,799,2397,7191
Now, list down the factors of 6783
:1,3,7,17,19,21,51,57,119,133,323,357,399,969,2261,6783
Greatest Common Factor
We found the factors 7191,6783 . The biggest common factor number is the GCF number.
So the greatest common factor 7191,6783 is 51.
Lets's calculate LCM of 686,8538
| 2 | 686, 8538 |
| 343, 4269 |
∴ So the LCM of the given numbers is 2 x 343 x 4269 = 2928534
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/2928534
Therefore, the GCF of Fractions 7191/686,6783/8538 is 51/2928534
Least Common Multiple of 686,8538 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 686,8538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(686,8538) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(686,8538) x common factors =2 x 1 = 2
LCM(686,8538) = ( 686 × 8538 ) / 2
LCM(686,8538) = 5857068 / 2
LCM(686,8538) = 2928534
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FAQs on GCF of Fractions of 7191/686, 6783/8538
1. What is the HCF of 7191,6783?
The HCF of 7191,6783 is 51
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 7191/686, 6783/8538?
Answer: GCF of Numerators as per given numbers 7191/686, 6783/8538 is
GCF of Numerators i.e. for 7191,6783 is 51
LCM of denominators i.e. for 686,8538 is 2928534.
Thus, GCF of Fractions is 51/2928534.Finally, GCF of Fractions for 7191/686, 6783/8538 is 51/2928534.