GCF of 68/114, 107/132, 556/589
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/114, 107/132, 556/589 i.e 1/77748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/114, 107/132, 556/589.
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 68/114,107/132,556/589?
Given fractions are 68/114,107/132,556/589
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 68/114,107/132,556/589, numerators are 68,107,556
Denominators are 114,132,589
The GCF of 68,107,556 is 1 .
LCM of 114,132,589 is 77748.
The greatest common factor of 68/114,107/132,556/589 = [GCF of 68,107,556]/[LCM of 114,132,589]= 1/77748
Therefore, the GCF of 68/114,107/132,556/589 is 1/77748.
To find the highest common factor of 68,107,556, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 107 are 1, 107
The factors of 556 are 1, 2, 4, 139, 278, 556
The HCF of 68,107,556 is 1.
Lets's calculate GCF of 68,107,556
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 68,107,556 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 107
:1,107
Now, list down the factors of 556
:1,2,4,139,278,556
Greatest Common Factor
We found the factors 68,107,556 . The biggest common factor number is the GCF number.
So the greatest common factor 68,107,556 is 1.
Lets's calculate LCM of 114,132,589
| 2 | 114, 132, 589 |
| 3 | 57, 66, 589 |
| 19 | 19, 22, 589 |
| 1, 22, 31 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 1 x 22 x 31 = 77748
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/77748
Therefore, the GCF of Fractions 68/114,107/132,556/589 is 1/77748
Least Common Multiple of 114,132,589 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 114,132,589 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(114,132,589) = 1
common factors(in case of two or more numbers have common factors) = 114
GCF(114,132,589) x common factors =1 x 114 = 114
LCM(114,132,589) = ( 114 × 132 × 589 ) / 114
LCM(114,132,589) = 8863272 / 114
LCM(114,132,589) = 77748
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 68/114, 107/132, 556/589
1. What is the HCF of 68,107,556?
The HCF of 68,107,556 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 68/114, 107/132, 556/589?
Answer: GCF of Numerators as per given numbers 68/114, 107/132, 556/589 is
GCF of Numerators i.e. for 68,107,556 is 1
LCM of denominators i.e. for 114,132,589 is 77748.
Thus, GCF of Fractions is 1/77748.Finally, GCF of Fractions for 68/114, 107/132, 556/589 is 1/77748.