Use our free GCF of Fractions Calculator tool to compute the GCF of 86/113, 678/741, 314/338 i.e 2/2177058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/113, 678/741, 314/338.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 86/113,678/741,314/338
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 86/113,678/741,314/338, numerators are 86,678,314
Denominators are 113,741,338
The GCF of 86,678,314 is 2 .
LCM of 113,741,338 is 2177058.
The greatest common factor of 86/113,678/741,314/338 = [GCF of 86,678,314]/[LCM of 113,741,338]= 2/2177058
Therefore, the GCF of 86/113,678/741,314/338 is 2/2177058.
To find the highest common factor of 86,678,314, 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 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 314 are 1, 2, 157, 314
The HCF of 86,678,314 is 2.
Lets's calculate GCF of 86,678,314
2 | 86, 678, 314 |
43, 339, 157 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 86,678,314 . The biggest common factor number is the GCF number.
So the greatest common factor 86,678,314 is 2.
Lets's calculate LCM of 113,741,338
13 | 113, 741, 338 |
113, 57, 26 |
∴ So the LCM of the given numbers is 13 x 113 x 57 x 26 = 2177058
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2177058
Therefore, the GCF of Fractions 86/113,678/741,314/338 is 2/2177058
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 113,741,338 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(113,741,338) = 1
common factors(in case of two or more numbers have common factors) = 13
GCF(113,741,338) x common factors =1 x 13 = 13
LCM(113,741,338) = ( 113 × 741 × 338 ) / 13
LCM(113,741,338) = 28301754 / 13
LCM(113,741,338) = 2177058
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 86,678,314?
The HCF of 86,678,314 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 86/113, 678/741, 314/338?
Answer: GCF of Numerators as per given numbers 86/113, 678/741, 314/338 is
GCF of Numerators i.e. for 86,678,314 is 2
LCM of denominators i.e. for 113,741,338 is 2177058.
Thus, GCF of Fractions is 2/2177058.Finally, GCF of Fractions for 86/113, 678/741, 314/338 is 2/2177058.