GCF of 461/414, 342/295
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 461/414, 342/295 i.e 1/122130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 461/414, 342/295.
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 461/414,342/295?
Given fractions are 461/414,342/295
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 461/414,342/295, numerators are 461,342
Denominators are 414,295
The GCF of 461,342 is 1 .
LCM of 414,295 is 122130.
The greatest common factor of 461/414,342/295 = [GCF of 461,342]/[LCM of 414,295]= 1/122130
Therefore, the GCF of 461/414,342/295 is 1/122130.
To find the highest common factor of 461,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 461 are 1, 461
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 461,342 is 1.
Lets's calculate GCF of 461,342
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 461,342 By Matching Biggest Common Factor Method
Now, list down the factors of 461
:1,461
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 461,342 . The biggest common factor number is the GCF number.
So the greatest common factor 461,342 is 1.
Lets's calculate LCM of 414,295
Given numbers has no common factors except 1. So, there LCM is their product i.e 122130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122130
Therefore, the GCF of Fractions 461/414,342/295 is 1/122130
Least Common Multiple of 414,295 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 414,295 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,295) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(414,295) x common factors =1 x 1 = 1
LCM(414,295) = ( 414 × 295 ) / 1
LCM(414,295) = 122130 / 1
LCM(414,295) = 122130
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FAQs on GCF of Fractions of 461/414, 342/295
1. What is the HCF of 461,342?
The HCF of 461,342 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 461/414, 342/295?
Answer: GCF of Numerators as per given numbers 461/414, 342/295 is
GCF of Numerators i.e. for 461,342 is 1
LCM of denominators i.e. for 414,295 is 122130.
Thus, GCF of Fractions is 1/122130.Finally, GCF of Fractions for 461/414, 342/295 is 1/122130.