GCF of 301/842, 1830/5754
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 301/842, 1830/5754 i.e 1/2422434 easily. The following is the detailed procedure to determine the greatest common factor of fractions 301/842, 1830/5754.
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 301/842,1830/5754?
Given fractions are 301/842,1830/5754
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 301/842,1830/5754, numerators are 301,1830
Denominators are 842,5754
The GCF of 301,1830 is 1 .
LCM of 842,5754 is 2422434.
The greatest common factor of 301/842,1830/5754 = [GCF of 301,1830]/[LCM of 842,5754]= 1/2422434
Therefore, the GCF of 301/842,1830/5754 is 1/2422434.
To find the highest common factor of 301,1830, we have to find the factors of both numbers and list the highest common factor.
The factors of 301 are 1, 7, 43, 301
The factors of 1830 are 1, 2, 3, 5, 6, 10, 15, 30, 61, 122, 183, 305, 366, 610, 915, 1830
The HCF of 301,1830 is 1.
Lets's calculate GCF of 301,1830
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 301,1830 By Matching Biggest Common Factor Method
Now, list down the factors of 301
:1,7,43,301
Now, list down the factors of 1830
:1,2,3,5,6,10,15,30,61,122,183,305,366,610,915,1830
Greatest Common Factor
We found the factors 301,1830 . The biggest common factor number is the GCF number.
So the greatest common factor 301,1830 is 1.
Lets's calculate LCM of 842,5754
| 2 | 842, 5754 |
| 421, 2877 |
∴ So the LCM of the given numbers is 2 x 421 x 2877 = 2422434
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2422434
Therefore, the GCF of Fractions 301/842,1830/5754 is 1/2422434
Least Common Multiple of 842,5754 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 842,5754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(842,5754) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(842,5754) x common factors =2 x 1 = 2
LCM(842,5754) = ( 842 × 5754 ) / 2
LCM(842,5754) = 4844868 / 2
LCM(842,5754) = 2422434
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FAQs on GCF of Fractions of 301/842, 1830/5754
1. What is the HCF of 301,1830?
The HCF of 301,1830 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 301/842, 1830/5754?
Answer: GCF of Numerators as per given numbers 301/842, 1830/5754 is
GCF of Numerators i.e. for 301,1830 is 1
LCM of denominators i.e. for 842,5754 is 2422434.
Thus, GCF of Fractions is 1/2422434.Finally, GCF of Fractions for 301/842, 1830/5754 is 1/2422434.