Use our free GCF of Fractions Calculator tool to compute the GCF of 256/684, 282/334 i.e 2/114228 easily. The following is the detailed procedure to determine the greatest common factor of fractions 256/684, 282/334.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 256/684,282/334
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 256/684,282/334, numerators are 256,282
Denominators are 684,334
The GCF of 256,282 is 2 .
LCM of 684,334 is 114228.
The greatest common factor of 256/684,282/334 = [GCF of 256,282]/[LCM of 684,334]= 2/114228
Therefore, the GCF of 256/684,282/334 is 2/114228.
To find the highest common factor of 256,282, 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 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 256,282 is 2.
Lets's calculate GCF of 256,282
2 | 256, 282 |
128, 141 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 256,282 . The biggest common factor number is the GCF number.
So the greatest common factor 256,282 is 2.
Lets's calculate LCM of 684,334
2 | 684, 334 |
342, 167 |
∴ So the LCM of the given numbers is 2 x 342 x 167 = 114228
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/114228
Therefore, the GCF of Fractions 256/684,282/334 is 2/114228
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 684,334 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,334) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(684,334) x common factors =2 x 1 = 2
LCM(684,334) = ( 684 × 334 ) / 2
LCM(684,334) = 228456 / 2
LCM(684,334) = 114228
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 256,282?
The HCF of 256,282 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 256/684, 282/334?
Answer: GCF of Numerators as per given numbers 256/684, 282/334 is
GCF of Numerators i.e. for 256,282 is 2
LCM of denominators i.e. for 684,334 is 114228.
Thus, GCF of Fractions is 2/114228.Finally, GCF of Fractions for 256/684, 282/334 is 2/114228.