GCF of 401/129, 342/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 401/129, 342/678 i.e 1/29154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 401/129, 342/678.
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 401/129,342/678?
Given fractions are 401/129,342/678
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 401/129,342/678, numerators are 401,342
Denominators are 129,678
The GCF of 401,342 is 1 .
LCM of 129,678 is 29154.
The greatest common factor of 401/129,342/678 = [GCF of 401,342]/[LCM of 129,678]= 1/29154
Therefore, the GCF of 401/129,342/678 is 1/29154.
To find the highest common factor of 401,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 401 are 1, 401
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 401,342 is 1.
Lets's calculate GCF of 401,342
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 401,342 By Matching Biggest Common Factor Method
Now, list down the factors of 401
:1,401
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 401,342 . The biggest common factor number is the GCF number.
So the greatest common factor 401,342 is 1.
Lets's calculate LCM of 129,678
| 3 | 129, 678 |
| 43, 226 |
∴ So the LCM of the given numbers is 3 x 43 x 226 = 29154
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29154
Therefore, the GCF of Fractions 401/129,342/678 is 1/29154
Least Common Multiple of 129,678 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 129,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(129,678) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(129,678) x common factors =3 x 1 = 3
LCM(129,678) = ( 129 × 678 ) / 3
LCM(129,678) = 87462 / 3
LCM(129,678) = 29154
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FAQs on GCF of Fractions of 401/129, 342/678
1. What is the HCF of 401,342?
The HCF of 401,342 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 401/129, 342/678?
Answer: GCF of Numerators as per given numbers 401/129, 342/678 is
GCF of Numerators i.e. for 401,342 is 1
LCM of denominators i.e. for 129,678 is 29154.
Thus, GCF of Fractions is 1/29154.Finally, GCF of Fractions for 401/129, 342/678 is 1/29154.