Use our free GCF of Fractions Calculator tool to compute the GCF of 20/77, 114/31, 131/674 i.e 1/1608838 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/77, 114/31, 131/674.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 20/77,114/31,131/674
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 20/77,114/31,131/674, numerators are 20,114,131
Denominators are 77,31,674
The GCF of 20,114,131 is 1 .
LCM of 77,31,674 is 1608838.
The greatest common factor of 20/77,114/31,131/674 = [GCF of 20,114,131]/[LCM of 77,31,674]= 1/1608838
Therefore, the GCF of 20/77,114/31,131/674 is 1/1608838.
To find the highest common factor of 20,114,131, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The factors of 131 are 1, 131
The HCF of 20,114,131 is 1.
Lets's calculate GCF of 20,114,131
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Now, list down the factors of 131
:1,131
Greatest Common Factor
We found the factors 20,114,131 . The biggest common factor number is the GCF number.
So the greatest common factor 20,114,131 is 1.
Lets's calculate LCM of 77,31,674
Given numbers has no common factors except 1. So, there LCM is their product i.e 1608838
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1608838
Therefore, the GCF of Fractions 20/77,114/31,131/674 is 1/1608838
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 77,31,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,31,674) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,31,674) x common factors =1 x 1 = 1
LCM(77,31,674) = ( 77 × 31 × 674 ) / 1
LCM(77,31,674) = 1608838 / 1
LCM(77,31,674) = 1608838
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 20,114,131?
The HCF of 20,114,131 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 20/77, 114/31, 131/674?
Answer: GCF of Numerators as per given numbers 20/77, 114/31, 131/674 is
GCF of Numerators i.e. for 20,114,131 is 1
LCM of denominators i.e. for 77,31,674 is 1608838.
Thus, GCF of Fractions is 1/1608838.Finally, GCF of Fractions for 20/77, 114/31, 131/674 is 1/1608838.