Use our free GCF of Fractions Calculator tool to compute the GCF of 43/320, 21/854, 688/135 i.e 1/3689280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/320, 21/854, 688/135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 43/320,21/854,688/135
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 43/320,21/854,688/135, numerators are 43,21,688
Denominators are 320,854,135
The GCF of 43,21,688 is 1 .
LCM of 320,854,135 is 3689280.
The greatest common factor of 43/320,21/854,688/135 = [GCF of 43,21,688]/[LCM of 320,854,135]= 1/3689280
Therefore, the GCF of 43/320,21/854,688/135 is 1/3689280.
To find the highest common factor of 43,21,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 21 are 1, 3, 7, 21
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 43,21,688 is 1.
Lets's calculate GCF of 43,21,688
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 43
:1,43
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 43,21,688 . The biggest common factor number is the GCF number.
So the greatest common factor 43,21,688 is 1.
Lets's calculate LCM of 320,854,135
2 | 320, 854, 135 |
5 | 160, 427, 135 |
32, 427, 27 |
∴ So the LCM of the given numbers is 2 x 5 x 32 x 427 x 27 = 3689280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3689280
Therefore, the GCF of Fractions 43/320,21/854,688/135 is 1/3689280
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 320,854,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,854,135) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(320,854,135) x common factors =1 x 10 = 10
LCM(320,854,135) = ( 320 × 854 × 135 ) / 10
LCM(320,854,135) = 36892800 / 10
LCM(320,854,135) = 3689280
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 43,21,688?
The HCF of 43,21,688 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 43/320, 21/854, 688/135?
Answer: GCF of Numerators as per given numbers 43/320, 21/854, 688/135 is
GCF of Numerators i.e. for 43,21,688 is 1
LCM of denominators i.e. for 320,854,135 is 3689280.
Thus, GCF of Fractions is 1/3689280.Finally, GCF of Fractions for 43/320, 21/854, 688/135 is 1/3689280.