GCF of 121/840, 285/343
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 121/840, 285/343 i.e 1/41160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 121/840, 285/343.
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 121/840,285/343?
Given fractions are 121/840,285/343
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 121/840,285/343, numerators are 121,285
Denominators are 840,343
The GCF of 121,285 is 1 .
LCM of 840,343 is 41160.
The greatest common factor of 121/840,285/343 = [GCF of 121,285]/[LCM of 840,343]= 1/41160
Therefore, the GCF of 121/840,285/343 is 1/41160.
To find the highest common factor of 121,285, we have to find the factors of both numbers and list the highest common factor.
The factors of 121 are 1, 11, 121
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The HCF of 121,285 is 1.
Lets's calculate GCF of 121,285
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 121,285 By Matching Biggest Common Factor Method
Now, list down the factors of 121
:1,11,121
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Greatest Common Factor
We found the factors 121,285 . The biggest common factor number is the GCF number.
So the greatest common factor 121,285 is 1.
Lets's calculate LCM of 840,343
| 7 | 840, 343 |
| 120, 49 |
∴ So the LCM of the given numbers is 7 x 120 x 49 = 41160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41160
Therefore, the GCF of Fractions 121/840,285/343 is 1/41160
Least Common Multiple of 840,343 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 840,343 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,343) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(840,343) x common factors =7 x 1 = 7
LCM(840,343) = ( 840 × 343 ) / 7
LCM(840,343) = 288120 / 7
LCM(840,343) = 41160
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FAQs on GCF of Fractions of 121/840, 285/343
1. What is the HCF of 121,285?
The HCF of 121,285 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 121/840, 285/343?
Answer: GCF of Numerators as per given numbers 121/840, 285/343 is
GCF of Numerators i.e. for 121,285 is 1
LCM of denominators i.e. for 840,343 is 41160.
Thus, GCF of Fractions is 1/41160.Finally, GCF of Fractions for 121/840, 285/343 is 1/41160.