GCF of 543/413, 5742/152
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 543/413, 5742/152 i.e 3/62776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 543/413, 5742/152.
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 543/413,5742/152?
Given fractions are 543/413,5742/152
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 543/413,5742/152, numerators are 543,5742
Denominators are 413,152
The GCF of 543,5742 is 3 .
LCM of 413,152 is 62776.
The greatest common factor of 543/413,5742/152 = [GCF of 543,5742]/[LCM of 413,152]= 3/62776
Therefore, the GCF of 543/413,5742/152 is 3/62776.
To find the highest common factor of 543,5742, we have to find the factors of both numbers and list the highest common factor.
The factors of 543 are 1, 3, 181, 543
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 543,5742 is 3.
Lets's calculate GCF of 543,5742
| 3 | 543, 5742 |
| 181, 1914 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 543,5742 By Matching Biggest Common Factor Method
Now, list down the factors of 543
:1,3,181,543
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 543,5742 . The biggest common factor number is the GCF number.
So the greatest common factor 543,5742 is 3.
Lets's calculate LCM of 413,152
Given numbers has no common factors except 1. So, there LCM is their product i.e 62776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/62776
Therefore, the GCF of Fractions 543/413,5742/152 is 3/62776
Least Common Multiple of 413,152 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 413,152 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,152) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,152) x common factors =1 x 1 = 1
LCM(413,152) = ( 413 × 152 ) / 1
LCM(413,152) = 62776 / 1
LCM(413,152) = 62776
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FAQs on GCF of Fractions of 543/413, 5742/152
1. What is the HCF of 543,5742?
The HCF of 543,5742 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 543/413, 5742/152?
Answer: GCF of Numerators as per given numbers 543/413, 5742/152 is
GCF of Numerators i.e. for 543,5742 is 3
LCM of denominators i.e. for 413,152 is 62776.
Thus, GCF of Fractions is 3/62776.Finally, GCF of Fractions for 543/413, 5742/152 is 3/62776.