GCF of 61/489, 731/319, 854/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 61/489, 731/319, 854/729 i.e 1/37905813 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/489, 731/319, 854/729.
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 61/489,731/319,854/729?
Given fractions are 61/489,731/319,854/729
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 61/489,731/319,854/729, numerators are 61,731,854
Denominators are 489,319,729
The GCF of 61,731,854 is 1 .
LCM of 489,319,729 is 37905813.
The greatest common factor of 61/489,731/319,854/729 = [GCF of 61,731,854]/[LCM of 489,319,729]= 1/37905813
Therefore, the GCF of 61/489,731/319,854/729 is 1/37905813.
To find the highest common factor of 61,731,854, we have to find the factors of both numbers and list the highest common factor.
The factors of 61 are 1, 61
The factors of 731 are 1, 17, 43, 731
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The HCF of 61,731,854 is 1.
Lets's calculate GCF of 61,731,854
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 61,731,854 By Matching Biggest Common Factor Method
Now, list down the factors of 61
:1,61
Now, list down the factors of 731
:1,17,43,731
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Greatest Common Factor
We found the factors 61,731,854 . The biggest common factor number is the GCF number.
So the greatest common factor 61,731,854 is 1.
Lets's calculate LCM of 489,319,729
| 3 | 489, 319, 729 |
| 163, 319, 243 |
∴ So the LCM of the given numbers is 3 x 163 x 319 x 243 = 37905813
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37905813
Therefore, the GCF of Fractions 61/489,731/319,854/729 is 1/37905813
Least Common Multiple of 489,319,729 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 489,319,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(489,319,729) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(489,319,729) x common factors =1 x 3 = 3
LCM(489,319,729) = ( 489 × 319 × 729 ) / 3
LCM(489,319,729) = 113717439 / 3
LCM(489,319,729) = 37905813
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FAQs on GCF of Fractions of 61/489, 731/319, 854/729
1. What is the HCF of 61,731,854?
The HCF of 61,731,854 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 61/489, 731/319, 854/729?
Answer: GCF of Numerators as per given numbers 61/489, 731/319, 854/729 is
GCF of Numerators i.e. for 61,731,854 is 1
LCM of denominators i.e. for 489,319,729 is 37905813.
Thus, GCF of Fractions is 1/37905813.Finally, GCF of Fractions for 61/489, 731/319, 854/729 is 1/37905813.