GCF of 543/214, 778/491
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 543/214, 778/491 i.e 1/105074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 543/214, 778/491.
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 543/214,778/491?
Given fractions are 543/214,778/491
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 543/214,778/491, numerators are 543,778
Denominators are 214,491
The GCF of 543,778 is 1 .
LCM of 214,491 is 105074.
The greatest common factor of 543/214,778/491 = [GCF of 543,778]/[LCM of 214,491]= 1/105074
Therefore, the GCF of 543/214,778/491 is 1/105074.
To find the highest common factor of 543,778, we have to find the factors of both numbers and list the highest common factor.
The factors of 543 are 1, 3, 181, 543
The factors of 778 are 1, 2, 389, 778
The HCF of 543,778 is 1.
Lets's calculate GCF of 543,778
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 543,778 By Matching Biggest Common Factor Method
Now, list down the factors of 543
:1,3,181,543
Now, list down the factors of 778
:1,2,389,778
Greatest Common Factor
We found the factors 543,778 . The biggest common factor number is the GCF number.
So the greatest common factor 543,778 is 1.
Lets's calculate LCM of 214,491
Given numbers has no common factors except 1. So, there LCM is their product i.e 105074
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105074
Therefore, the GCF of Fractions 543/214,778/491 is 1/105074
Least Common Multiple of 214,491 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 214,491 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,491) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(214,491) x common factors =1 x 1 = 1
LCM(214,491) = ( 214 × 491 ) / 1
LCM(214,491) = 105074 / 1
LCM(214,491) = 105074
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FAQs on GCF of Fractions of 543/214, 778/491
1. What is the HCF of 543,778?
The HCF of 543,778 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 543/214, 778/491?
Answer: GCF of Numerators as per given numbers 543/214, 778/491 is
GCF of Numerators i.e. for 543,778 is 1
LCM of denominators i.e. for 214,491 is 105074.
Thus, GCF of Fractions is 1/105074.Finally, GCF of Fractions for 543/214, 778/491 is 1/105074.