GCF of 766/313, 742/589
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 766/313, 742/589 i.e 2/184357 easily. The following is the detailed procedure to determine the greatest common factor of fractions 766/313, 742/589.
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 766/313,742/589?
Given fractions are 766/313,742/589
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 766/313,742/589, numerators are 766,742
Denominators are 313,589
The GCF of 766,742 is 2 .
LCM of 313,589 is 184357.
The greatest common factor of 766/313,742/589 = [GCF of 766,742]/[LCM of 313,589]= 2/184357
Therefore, the GCF of 766/313,742/589 is 2/184357.
To find the highest common factor of 766,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 766 are 1, 2, 383, 766
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 766,742 is 2.
Lets's calculate GCF of 766,742
| 2 | 766, 742 |
| 383, 371 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 766,742 By Matching Biggest Common Factor Method
Now, list down the factors of 766
:1,2,383,766
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 766,742 . The biggest common factor number is the GCF number.
So the greatest common factor 766,742 is 2.
Lets's calculate LCM of 313,589
Given numbers has no common factors except 1. So, there LCM is their product i.e 184357
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/184357
Therefore, the GCF of Fractions 766/313,742/589 is 2/184357
Least Common Multiple of 313,589 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 313,589 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(313,589) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(313,589) x common factors =1 x 1 = 1
LCM(313,589) = ( 313 × 589 ) / 1
LCM(313,589) = 184357 / 1
LCM(313,589) = 184357
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FAQs on GCF of Fractions of 766/313, 742/589
1. What is the HCF of 766,742?
The HCF of 766,742 is 2
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 766/313, 742/589?
Answer: GCF of Numerators as per given numbers 766/313, 742/589 is
GCF of Numerators i.e. for 766,742 is 2
LCM of denominators i.e. for 313,589 is 184357.
Thus, GCF of Fractions is 2/184357.Finally, GCF of Fractions for 766/313, 742/589 is 2/184357.