Use our free GCF of Fractions Calculator tool to compute the GCF of 128/898, 704/386 i.e 64/173314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 128/898, 704/386.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 128/898,704/386
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 128/898,704/386, numerators are 128,704
Denominators are 898,386
The GCF of 128,704 is 64 .
LCM of 898,386 is 173314.
The greatest common factor of 128/898,704/386 = [GCF of 128,704]/[LCM of 898,386]= 64/173314
Therefore, the GCF of 128/898,704/386 is 64/173314.
To find the highest common factor of 128,704, we have to find the factors of both numbers and list the highest common factor.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The HCF of 128,704 is 64.
Lets's calculate GCF of 128,704
2 | 128, 704 |
2 | 64, 352 |
2 | 32, 176 |
2 | 16, 88 |
2 | 8, 44 |
2 | 4, 22 |
2, 11 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Greatest Common Factor
We found the factors 128,704 . The biggest common factor number is the GCF number.
So the greatest common factor 128,704 is 64.
Lets's calculate LCM of 898,386
2 | 898, 386 |
449, 193 |
∴ So the LCM of the given numbers is 2 x 449 x 193 = 173314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/173314
Therefore, the GCF of Fractions 128/898,704/386 is 64/173314
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 898,386 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(898,386) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(898,386) x common factors =2 x 1 = 2
LCM(898,386) = ( 898 × 386 ) / 2
LCM(898,386) = 346628 / 2
LCM(898,386) = 173314
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 128,704?
The HCF of 128,704 is 64
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 128/898, 704/386?
Answer: GCF of Numerators as per given numbers 128/898, 704/386 is
GCF of Numerators i.e. for 128,704 is 64
LCM of denominators i.e. for 898,386 is 173314.
Thus, GCF of Fractions is 64/173314.Finally, GCF of Fractions for 128/898, 704/386 is 64/173314.