GCF of 243/142, 729/988
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 243/142, 729/988 i.e 243/70148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 243/142, 729/988.
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 243/142,729/988?
Given fractions are 243/142,729/988
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 243/142,729/988, numerators are 243,729
Denominators are 142,988
The GCF of 243,729 is 243 .
LCM of 142,988 is 70148.
The greatest common factor of 243/142,729/988 = [GCF of 243,729]/[LCM of 142,988]= 243/70148
Therefore, the GCF of 243/142,729/988 is 243/70148.
To find the highest common factor of 243,729, we have to find the factors of both numbers and list the highest common factor.
The factors of 243 are 1, 3, 9, 27, 81, 243
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The HCF of 243,729 is 243.
Lets's calculate GCF of 243,729
| 3 | 243, 729 |
| 3 | 81, 243 |
| 3 | 27, 81 |
| 3 | 9, 27 |
| 3 | 3, 9 |
| 1, 3 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 3 x 3 = 243
Greatest Common Factor of 243,729 By Matching Biggest Common Factor Method
Now, list down the factors of 243
:1,3,9,27,81,243
Now, list down the factors of 729
:1,3,9,27,81,243,729
Greatest Common Factor
We found the factors 243,729 . The biggest common factor number is the GCF number.
So the greatest common factor 243,729 is 243.
Lets's calculate LCM of 142,988
| 2 | 142, 988 |
| 71, 494 |
∴ So the LCM of the given numbers is 2 x 71 x 494 = 70148
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 243/70148
Therefore, the GCF of Fractions 243/142,729/988 is 243/70148
Least Common Multiple of 142,988 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 142,988 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,988) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,988) x common factors =2 x 1 = 2
LCM(142,988) = ( 142 × 988 ) / 2
LCM(142,988) = 140296 / 2
LCM(142,988) = 70148
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FAQs on GCF of Fractions of 243/142, 729/988
1. What is the HCF of 243,729?
The HCF of 243,729 is 243
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 243/142, 729/988?
Answer: GCF of Numerators as per given numbers 243/142, 729/988 is
GCF of Numerators i.e. for 243,729 is 243
LCM of denominators i.e. for 142,988 is 70148.
Thus, GCF of Fractions is 243/70148.Finally, GCF of Fractions for 243/142, 729/988 is 243/70148.