GCF of 434/116, 1419/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 434/116, 1419/582 i.e 1/33756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 434/116, 1419/582.
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 434/116,1419/582?
Given fractions are 434/116,1419/582
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 434/116,1419/582, numerators are 434,1419
Denominators are 116,582
The GCF of 434,1419 is 1 .
LCM of 116,582 is 33756.
The greatest common factor of 434/116,1419/582 = [GCF of 434,1419]/[LCM of 116,582]= 1/33756
Therefore, the GCF of 434/116,1419/582 is 1/33756.
To find the highest common factor of 434,1419, 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 1419 are 1, 3, 11, 33, 43, 129, 473, 1419
The HCF of 434,1419 is 1.
Lets's calculate GCF of 434,1419
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 434,1419 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 1419
:1,3,11,33,43,129,473,1419
Greatest Common Factor
We found the factors 434,1419 . The biggest common factor number is the GCF number.
So the greatest common factor 434,1419 is 1.
Lets's calculate LCM of 116,582
| 2 | 116, 582 |
| 58, 291 |
∴ So the LCM of the given numbers is 2 x 58 x 291 = 33756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33756
Therefore, the GCF of Fractions 434/116,1419/582 is 1/33756
Least Common Multiple of 116,582 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 116,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(116,582) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(116,582) x common factors =2 x 1 = 2
LCM(116,582) = ( 116 × 582 ) / 2
LCM(116,582) = 67512 / 2
LCM(116,582) = 33756
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FAQs on GCF of Fractions of 434/116, 1419/582
1. What is the HCF of 434,1419?
The HCF of 434,1419 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 434/116, 1419/582?
Answer: GCF of Numerators as per given numbers 434/116, 1419/582 is
GCF of Numerators i.e. for 434,1419 is 1
LCM of denominators i.e. for 116,582 is 33756.
Thus, GCF of Fractions is 1/33756.Finally, GCF of Fractions for 434/116, 1419/582 is 1/33756.