GCF of 6750/546, 8128/7723
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6750/546, 8128/7723 i.e 2/4216758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6750/546, 8128/7723.
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 6750/546,8128/7723?
Given fractions are 6750/546,8128/7723
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 6750/546,8128/7723, numerators are 6750,8128
Denominators are 546,7723
The GCF of 6750,8128 is 2 .
LCM of 546,7723 is 4216758.
The greatest common factor of 6750/546,8128/7723 = [GCF of 6750,8128]/[LCM of 546,7723]= 2/4216758
Therefore, the GCF of 6750/546,8128/7723 is 2/4216758.
To find the highest common factor of 6750,8128, we have to find the factors of both numbers and list the highest common factor.
The factors of 6750 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 125, 135, 150, 225, 250, 270, 375, 450, 675, 750, 1125, 1350, 2250, 3375, 6750
The factors of 8128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, 8128
The HCF of 6750,8128 is 2.
Lets's calculate GCF of 6750,8128
| 2 | 6750, 8128 |
| 3375, 4064 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6750,8128 By Matching Biggest Common Factor Method
Now, list down the factors of 6750
:1,2,3,5,6,9,10,15,18,25,27,30,45,50,54,75,90,125,135,150,225,250,270,375,450,675,750,1125,1350,2250,3375,6750
Now, list down the factors of 8128
:1,2,4,8,16,32,64,127,254,508,1016,2032,4064,8128
Greatest Common Factor
We found the factors 6750,8128 . The biggest common factor number is the GCF number.
So the greatest common factor 6750,8128 is 2.
Lets's calculate LCM of 546,7723
Given numbers has no common factors except 1. So, there LCM is their product i.e 4216758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4216758
Therefore, the GCF of Fractions 6750/546,8128/7723 is 2/4216758
Least Common Multiple of 546,7723 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 546,7723 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,7723) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(546,7723) x common factors =1 x 1 = 1
LCM(546,7723) = ( 546 × 7723 ) / 1
LCM(546,7723) = 4216758 / 1
LCM(546,7723) = 4216758
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FAQs on GCF of Fractions of 6750/546, 8128/7723
1. What is the HCF of 6750,8128?
The HCF of 6750,8128 is 2
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 6750/546, 8128/7723?
Answer: GCF of Numerators as per given numbers 6750/546, 8128/7723 is
GCF of Numerators i.e. for 6750,8128 is 2
LCM of denominators i.e. for 546,7723 is 4216758.
Thus, GCF of Fractions is 2/4216758.Finally, GCF of Fractions for 6750/546, 8128/7723 is 2/4216758.