GCF of 8016/386, 5742/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8016/386, 5742/578 i.e 6/111554 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8016/386, 5742/578.
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 8016/386,5742/578?
Given fractions are 8016/386,5742/578
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 8016/386,5742/578, numerators are 8016,5742
Denominators are 386,578
The GCF of 8016,5742 is 6 .
LCM of 386,578 is 111554.
The greatest common factor of 8016/386,5742/578 = [GCF of 8016,5742]/[LCM of 386,578]= 6/111554
Therefore, the GCF of 8016/386,5742/578 is 6/111554.
To find the highest common factor of 8016,5742, we have to find the factors of both numbers and list the highest common factor.
The factors of 8016 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 167, 334, 501, 668, 1002, 1336, 2004, 2672, 4008, 8016
The factors of 5742 are 1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742
The HCF of 8016,5742 is 6.
Lets's calculate GCF of 8016,5742
| 2 | 8016, 5742 |
| 3 | 4008, 2871 |
| 1336, 957 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 8016,5742 By Matching Biggest Common Factor Method
Now, list down the factors of 8016
:1,2,3,4,6,8,12,16,24,48,167,334,501,668,1002,1336,2004,2672,4008,8016
Now, list down the factors of 5742
:1,2,3,6,9,11,18,22,29,33,58,66,87,99,174,198,261,319,522,638,957,1914,2871,5742
Greatest Common Factor
We found the factors 8016,5742 . The biggest common factor number is the GCF number.
So the greatest common factor 8016,5742 is 6.
Lets's calculate LCM of 386,578
| 2 | 386, 578 |
| 193, 289 |
∴ So the LCM of the given numbers is 2 x 193 x 289 = 111554
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/111554
Therefore, the GCF of Fractions 8016/386,5742/578 is 6/111554
Least Common Multiple of 386,578 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 386,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(386,578) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(386,578) x common factors =2 x 1 = 2
LCM(386,578) = ( 386 × 578 ) / 2
LCM(386,578) = 223108 / 2
LCM(386,578) = 111554
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FAQs on GCF of Fractions of 8016/386, 5742/578
1. What is the HCF of 8016,5742?
The HCF of 8016,5742 is 6
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 8016/386, 5742/578?
Answer: GCF of Numerators as per given numbers 8016/386, 5742/578 is
GCF of Numerators i.e. for 8016,5742 is 6
LCM of denominators i.e. for 386,578 is 111554.
Thus, GCF of Fractions is 6/111554.Finally, GCF of Fractions for 8016/386, 5742/578 is 6/111554.