GCF of 820/45, 138/86, 243/828
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 820/45, 138/86, 243/828 i.e 1/178020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 820/45, 138/86, 243/828.
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 820/45,138/86,243/828?
Given fractions are 820/45,138/86,243/828
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 820/45,138/86,243/828, numerators are 820,138,243
Denominators are 45,86,828
The GCF of 820,138,243 is 1 .
LCM of 45,86,828 is 178020.
The greatest common factor of 820/45,138/86,243/828 = [GCF of 820,138,243]/[LCM of 45,86,828]= 1/178020
Therefore, the GCF of 820/45,138/86,243/828 is 1/178020.
To find the highest common factor of 820,138,243, we have to find the factors of both numbers and list the highest common factor.
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The factors of 243 are 1, 3, 9, 27, 81, 243
The HCF of 820,138,243 is 1.
Lets's calculate GCF of 820,138,243
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 820,138,243 By Matching Biggest Common Factor Method
Now, list down the factors of 820
:1,2,4,5,10,20,41,82,164,205,410,820
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Now, list down the factors of 243
:1,3,9,27,81,243
Greatest Common Factor
We found the factors 820,138,243 . The biggest common factor number is the GCF number.
So the greatest common factor 820,138,243 is 1.
Lets's calculate LCM of 45,86,828
| 2 | 45, 86, 828 |
| 3 | 45, 43, 414 |
| 3 | 15, 43, 138 |
| 5, 43, 46 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 43 x 46 = 178020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/178020
Therefore, the GCF of Fractions 820/45,138/86,243/828 is 1/178020
Least Common Multiple of 45,86,828 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 45,86,828 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,86,828) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(45,86,828) x common factors =1 x 18 = 18
LCM(45,86,828) = ( 45 × 86 × 828 ) / 18
LCM(45,86,828) = 3204360 / 18
LCM(45,86,828) = 178020
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FAQs on GCF of Fractions of 820/45, 138/86, 243/828
1. What is the HCF of 820,138,243?
The HCF of 820,138,243 is 1
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 820/45, 138/86, 243/828?
Answer: GCF of Numerators as per given numbers 820/45, 138/86, 243/828 is
GCF of Numerators i.e. for 820,138,243 is 1
LCM of denominators i.e. for 45,86,828 is 178020.
Thus, GCF of Fractions is 1/178020.Finally, GCF of Fractions for 820/45, 138/86, 243/828 is 1/178020.