Use our free GCF of Fractions Calculator tool to compute the GCF of 154/190, 340/729 i.e 2/138510 easily. The following is the detailed procedure to determine the greatest common factor of fractions 154/190, 340/729.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 154/190,340/729
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 154/190,340/729, numerators are 154,340
Denominators are 190,729
The GCF of 154,340 is 2 .
LCM of 190,729 is 138510.
The greatest common factor of 154/190,340/729 = [GCF of 154,340]/[LCM of 190,729]= 2/138510
Therefore, the GCF of 154/190,340/729 is 2/138510.
To find the highest common factor of 154,340, we have to find the factors of both numbers and list the highest common factor.
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The HCF of 154,340 is 2.
Lets's calculate GCF of 154,340
2 | 154, 340 |
77, 170 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Now, list down the factors of 340
:1,2,4,5,10,17,20,34,68,85,170,340
Greatest Common Factor
We found the factors 154,340 . The biggest common factor number is the GCF number.
So the greatest common factor 154,340 is 2.
Lets's calculate LCM of 190,729
Given numbers has no common factors except 1. So, there LCM is their product i.e 138510
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/138510
Therefore, the GCF of Fractions 154/190,340/729 is 2/138510
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 190,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(190,729) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(190,729) x common factors =1 x 1 = 1
LCM(190,729) = ( 190 × 729 ) / 1
LCM(190,729) = 138510 / 1
LCM(190,729) = 138510
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 154,340?
The HCF of 154,340 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 154/190, 340/729?
Answer: GCF of Numerators as per given numbers 154/190, 340/729 is
GCF of Numerators i.e. for 154,340 is 2
LCM of denominators i.e. for 190,729 is 138510.
Thus, GCF of Fractions is 2/138510.Finally, GCF of Fractions for 154/190, 340/729 is 2/138510.