GCF of 434/305, 1778/466
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 434/305, 1778/466 i.e 14/142130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 434/305, 1778/466.
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 434/305,1778/466?
Given fractions are 434/305,1778/466
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 434/305,1778/466, numerators are 434,1778
Denominators are 305,466
The GCF of 434,1778 is 14 .
LCM of 305,466 is 142130.
The greatest common factor of 434/305,1778/466 = [GCF of 434,1778]/[LCM of 305,466]= 14/142130
Therefore, the GCF of 434/305,1778/466 is 14/142130.
To find the highest common factor of 434,1778, we have to find the factors of both numbers and list the highest common factor.
The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434
The factors of 1778 are 1, 2, 7, 14, 127, 254, 889, 1778
The HCF of 434,1778 is 14.
Lets's calculate GCF of 434,1778
| 2 | 434, 1778 |
| 7 | 217, 889 |
| 31, 127 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 434,1778 By Matching Biggest Common Factor Method
Now, list down the factors of 434
:1,2,7,14,31,62,217,434
Now, list down the factors of 1778
:1,2,7,14,127,254,889,1778
Greatest Common Factor
We found the factors 434,1778 . The biggest common factor number is the GCF number.
So the greatest common factor 434,1778 is 14.
Lets's calculate LCM of 305,466
Given numbers has no common factors except 1. So, there LCM is their product i.e 142130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/142130
Therefore, the GCF of Fractions 434/305,1778/466 is 14/142130
Least Common Multiple of 305,466 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 305,466 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,466) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(305,466) x common factors =1 x 1 = 1
LCM(305,466) = ( 305 × 466 ) / 1
LCM(305,466) = 142130 / 1
LCM(305,466) = 142130
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FAQs on GCF of Fractions of 434/305, 1778/466
1. What is the HCF of 434,1778?
The HCF of 434,1778 is 14
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 434/305, 1778/466?
Answer: GCF of Numerators as per given numbers 434/305, 1778/466 is
GCF of Numerators i.e. for 434,1778 is 14
LCM of denominators i.e. for 305,466 is 142130.
Thus, GCF of Fractions is 14/142130.Finally, GCF of Fractions for 434/305, 1778/466 is 14/142130.