GCF of 1729/491, 5470/1978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1729/491, 5470/1978 i.e 1/971198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1729/491, 5470/1978.
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 1729/491,5470/1978?
Given fractions are 1729/491,5470/1978
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 1729/491,5470/1978, numerators are 1729,5470
Denominators are 491,1978
The GCF of 1729,5470 is 1 .
LCM of 491,1978 is 971198.
The greatest common factor of 1729/491,5470/1978 = [GCF of 1729,5470]/[LCM of 491,1978]= 1/971198
Therefore, the GCF of 1729/491,5470/1978 is 1/971198.
To find the highest common factor of 1729,5470, we have to find the factors of both numbers and list the highest common factor.
The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729
The factors of 5470 are 1, 2, 5, 10, 547, 1094, 2735, 5470
The HCF of 1729,5470 is 1.
Lets's calculate GCF of 1729,5470
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1729,5470 By Matching Biggest Common Factor Method
Now, list down the factors of 1729
:1,7,13,19,91,133,247,1729
Now, list down the factors of 5470
:1,2,5,10,547,1094,2735,5470
Greatest Common Factor
We found the factors 1729,5470 . The biggest common factor number is the GCF number.
So the greatest common factor 1729,5470 is 1.
Lets's calculate LCM of 491,1978
Given numbers has no common factors except 1. So, there LCM is their product i.e 971198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/971198
Therefore, the GCF of Fractions 1729/491,5470/1978 is 1/971198
Least Common Multiple of 491,1978 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 491,1978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(491,1978) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(491,1978) x common factors =1 x 1 = 1
LCM(491,1978) = ( 491 × 1978 ) / 1
LCM(491,1978) = 971198 / 1
LCM(491,1978) = 971198
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FAQs on GCF of Fractions of 1729/491, 5470/1978
1. What is the HCF of 1729,5470?
The HCF of 1729,5470 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 1729/491, 5470/1978?
Answer: GCF of Numerators as per given numbers 1729/491, 5470/1978 is
GCF of Numerators i.e. for 1729,5470 is 1
LCM of denominators i.e. for 491,1978 is 971198.
Thus, GCF of Fractions is 1/971198.Finally, GCF of Fractions for 1729/491, 5470/1978 is 1/971198.