Use our free GCF of Fractions Calculator tool to compute the GCF of 340/87, 260/192 i.e 20/5568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/87, 260/192.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 340/87,260/192
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 340/87,260/192, numerators are 340,260
Denominators are 87,192
The GCF of 340,260 is 20 .
LCM of 87,192 is 5568.
The greatest common factor of 340/87,260/192 = [GCF of 340,260]/[LCM of 87,192]= 20/5568
Therefore, the GCF of 340/87,260/192 is 20/5568.
To find the highest common factor of 340,260, we have to find the factors of both numbers and list the highest common factor.
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The HCF of 340,260 is 20.
Lets's calculate GCF of 340,260
2 | 340, 260 |
2 | 170, 130 |
5 | 85, 65 |
17, 13 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 340
:1,2,4,5,10,17,20,34,68,85,170,340
Now, list down the factors of 260
:1,2,4,5,10,13,20,26,52,65,130,260
Greatest Common Factor
We found the factors 340,260 . The biggest common factor number is the GCF number.
So the greatest common factor 340,260 is 20.
Lets's calculate LCM of 87,192
3 | 87, 192 |
29, 64 |
∴ So the LCM of the given numbers is 3 x 29 x 64 = 5568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/5568
Therefore, the GCF of Fractions 340/87,260/192 is 20/5568
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 87,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,192) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(87,192) x common factors =3 x 1 = 3
LCM(87,192) = ( 87 × 192 ) / 3
LCM(87,192) = 16704 / 3
LCM(87,192) = 5568
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 340,260?
The HCF of 340,260 is 20
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 340/87, 260/192?
Answer: GCF of Numerators as per given numbers 340/87, 260/192 is
GCF of Numerators i.e. for 340,260 is 20
LCM of denominators i.e. for 87,192 is 5568.
Thus, GCF of Fractions is 20/5568.Finally, GCF of Fractions for 340/87, 260/192 is 20/5568.