Use our free GCF of Fractions Calculator tool to compute the GCF of 426/828, 512/314 i.e 2/129996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 426/828, 512/314.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 426/828,512/314
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 426/828,512/314, numerators are 426,512
Denominators are 828,314
The GCF of 426,512 is 2 .
LCM of 828,314 is 129996.
The greatest common factor of 426/828,512/314 = [GCF of 426,512]/[LCM of 828,314]= 2/129996
Therefore, the GCF of 426/828,512/314 is 2/129996.
To find the highest common factor of 426,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 426,512 is 2.
Lets's calculate GCF of 426,512
2 | 426, 512 |
213, 256 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 426
:1,2,3,6,71,142,213,426
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 426,512 . The biggest common factor number is the GCF number.
So the greatest common factor 426,512 is 2.
Lets's calculate LCM of 828,314
2 | 828, 314 |
414, 157 |
∴ So the LCM of the given numbers is 2 x 414 x 157 = 129996
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/129996
Therefore, the GCF of Fractions 426/828,512/314 is 2/129996
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 828,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(828,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(828,314) x common factors =2 x 1 = 2
LCM(828,314) = ( 828 × 314 ) / 2
LCM(828,314) = 259992 / 2
LCM(828,314) = 129996
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 426,512?
The HCF of 426,512 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 426/828, 512/314?
Answer: GCF of Numerators as per given numbers 426/828, 512/314 is
GCF of Numerators i.e. for 426,512 is 2
LCM of denominators i.e. for 828,314 is 129996.
Thus, GCF of Fractions is 2/129996.Finally, GCF of Fractions for 426/828, 512/314 is 2/129996.