GCF of 789/543, 1470/591
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 789/543, 1470/591 i.e 3/106971 easily. The following is the detailed procedure to determine the greatest common factor of fractions 789/543, 1470/591.
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 789/543,1470/591?
Given fractions are 789/543,1470/591
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 789/543,1470/591, numerators are 789,1470
Denominators are 543,591
The GCF of 789,1470 is 3 .
LCM of 543,591 is 106971.
The greatest common factor of 789/543,1470/591 = [GCF of 789,1470]/[LCM of 543,591]= 3/106971
Therefore, the GCF of 789/543,1470/591 is 3/106971.
To find the highest common factor of 789,1470, we have to find the factors of both numbers and list the highest common factor.
The factors of 789 are 1, 3, 263, 789
The factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470
The HCF of 789,1470 is 3.
Lets's calculate GCF of 789,1470
| 3 | 789, 1470 |
| 263, 490 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 789,1470 By Matching Biggest Common Factor Method
Now, list down the factors of 789
:1,3,263,789
Now, list down the factors of 1470
:1,2,3,5,6,7,10,14,15,21,30,35,42,49,70,98,105,147,210,245,294,490,735,1470
Greatest Common Factor
We found the factors 789,1470 . The biggest common factor number is the GCF number.
So the greatest common factor 789,1470 is 3.
Lets's calculate LCM of 543,591
| 3 | 543, 591 |
| 181, 197 |
∴ So the LCM of the given numbers is 3 x 181 x 197 = 106971
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/106971
Therefore, the GCF of Fractions 789/543,1470/591 is 3/106971
Least Common Multiple of 543,591 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 543,591 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(543,591) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(543,591) x common factors =3 x 1 = 3
LCM(543,591) = ( 543 × 591 ) / 3
LCM(543,591) = 320913 / 3
LCM(543,591) = 106971
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FAQs on GCF of Fractions of 789/543, 1470/591
1. What is the HCF of 789,1470?
The HCF of 789,1470 is 3
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 789/543, 1470/591?
Answer: GCF of Numerators as per given numbers 789/543, 1470/591 is
GCF of Numerators i.e. for 789,1470 is 3
LCM of denominators i.e. for 543,591 is 106971.
Thus, GCF of Fractions is 3/106971.Finally, GCF of Fractions for 789/543, 1470/591 is 3/106971.