GCF of 342/320, 221/965
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/320, 221/965 i.e 1/61760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/320, 221/965.
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 342/320,221/965?
Given fractions are 342/320,221/965
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 342/320,221/965, numerators are 342,221
Denominators are 320,965
The GCF of 342,221 is 1 .
LCM of 320,965 is 61760.
The greatest common factor of 342/320,221/965 = [GCF of 342,221]/[LCM of 320,965]= 1/61760
Therefore, the GCF of 342/320,221/965 is 1/61760.
To find the highest common factor of 342,221, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 221 are 1, 13, 17, 221
The HCF of 342,221 is 1.
Lets's calculate GCF of 342,221
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 342,221 By Matching Biggest Common Factor Method
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 221
:1,13,17,221
Greatest Common Factor
We found the factors 342,221 . The biggest common factor number is the GCF number.
So the greatest common factor 342,221 is 1.
Lets's calculate LCM of 320,965
| 5 | 320, 965 |
| 64, 193 |
∴ So the LCM of the given numbers is 5 x 64 x 193 = 61760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/61760
Therefore, the GCF of Fractions 342/320,221/965 is 1/61760
Least Common Multiple of 320,965 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 320,965 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,965) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(320,965) x common factors =5 x 1 = 5
LCM(320,965) = ( 320 × 965 ) / 5
LCM(320,965) = 308800 / 5
LCM(320,965) = 61760
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FAQs on GCF of Fractions of 342/320, 221/965
1. What is the HCF of 342,221?
The HCF of 342,221 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 342/320, 221/965?
Answer: GCF of Numerators as per given numbers 342/320, 221/965 is
GCF of Numerators i.e. for 342,221 is 1
LCM of denominators i.e. for 320,965 is 61760.
Thus, GCF of Fractions is 1/61760.Finally, GCF of Fractions for 342/320, 221/965 is 1/61760.