Use our free GCF of Fractions Calculator tool to compute the GCF of 256/142, 692/734 i.e 4/52114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 256/142, 692/734.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 256/142,692/734
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 256/142,692/734, numerators are 256,692
Denominators are 142,734
The GCF of 256,692 is 4 .
LCM of 142,734 is 52114.
The greatest common factor of 256/142,692/734 = [GCF of 256,692]/[LCM of 142,734]= 4/52114
Therefore, the GCF of 256/142,692/734 is 4/52114.
To find the highest common factor of 256,692, we have to find the factors of both numbers and list the highest common factor.
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The factors of 692 are 1, 2, 4, 173, 346, 692
The HCF of 256,692 is 4.
Lets's calculate GCF of 256,692
2 | 256, 692 |
2 | 128, 346 |
64, 173 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Now, list down the factors of 692
:1,2,4,173,346,692
Greatest Common Factor
We found the factors 256,692 . The biggest common factor number is the GCF number.
So the greatest common factor 256,692 is 4.
Lets's calculate LCM of 142,734
2 | 142, 734 |
71, 367 |
∴ So the LCM of the given numbers is 2 x 71 x 367 = 52114
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/52114
Therefore, the GCF of Fractions 256/142,692/734 is 4/52114
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 142,734 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,734) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,734) x common factors =2 x 1 = 2
LCM(142,734) = ( 142 × 734 ) / 2
LCM(142,734) = 104228 / 2
LCM(142,734) = 52114
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 256,692?
The HCF of 256,692 is 4
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 256/142, 692/734?
Answer: GCF of Numerators as per given numbers 256/142, 692/734 is
GCF of Numerators i.e. for 256,692 is 4
LCM of denominators i.e. for 142,734 is 52114.
Thus, GCF of Fractions is 4/52114.Finally, GCF of Fractions for 256/142, 692/734 is 4/52114.