Use our free GCF of Fractions Calculator tool to compute the GCF of 86/29, 69/54, 340/18 i.e 1/1566 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/29, 69/54, 340/18.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 86/29,69/54,340/18
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 86/29,69/54,340/18, numerators are 86,69,340
Denominators are 29,54,18
The GCF of 86,69,340 is 1 .
LCM of 29,54,18 is 1566.
The greatest common factor of 86/29,69/54,340/18 = [GCF of 86,69,340]/[LCM of 29,54,18]= 1/1566
Therefore, the GCF of 86/29,69/54,340/18 is 1/1566.
To find the highest common factor of 86,69,340, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 69 are 1, 3, 23, 69
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The HCF of 86,69,340 is 1.
Lets's calculate GCF of 86,69,340
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 69
:1,3,23,69
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 86,69,340 . The biggest common factor number is the GCF number.
So the greatest common factor 86,69,340 is 1.
Lets's calculate LCM of 29,54,18
2 | 29, 54, 18 |
3 | 29, 27, 9 |
3 | 29, 3, 9 |
29, 1, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 29 x 1 x 3 = 1566
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1566
Therefore, the GCF of Fractions 86/29,69/54,340/18 is 1/1566
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 29,54,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,54,18) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(29,54,18) x common factors =1 x 18 = 18
LCM(29,54,18) = ( 29 × 54 × 18 ) / 18
LCM(29,54,18) = 28188 / 18
LCM(29,54,18) = 1566
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 86,69,340?
The HCF of 86,69,340 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 86/29, 69/54, 340/18?
Answer: GCF of Numerators as per given numbers 86/29, 69/54, 340/18 is
GCF of Numerators i.e. for 86,69,340 is 1
LCM of denominators i.e. for 29,54,18 is 1566.
Thus, GCF of Fractions is 1/1566.Finally, GCF of Fractions for 86/29, 69/54, 340/18 is 1/1566.