Use our free GCF of Fractions Calculator tool to compute the GCF of 392/668, 342/812 i.e 2/135604 easily. The following is the detailed procedure to determine the greatest common factor of fractions 392/668, 342/812.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 392/668,342/812
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 392/668,342/812, numerators are 392,342
Denominators are 668,812
The GCF of 392,342 is 2 .
LCM of 668,812 is 135604.
The greatest common factor of 392/668,342/812 = [GCF of 392,342]/[LCM of 668,812]= 2/135604
Therefore, the GCF of 392/668,342/812 is 2/135604.
To find the highest common factor of 392,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 392,342 is 2.
Lets's calculate GCF of 392,342
2 | 392, 342 |
196, 171 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 392
:1,2,4,7,8,14,28,49,56,98,196,392
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 392,342 . The biggest common factor number is the GCF number.
So the greatest common factor 392,342 is 2.
Lets's calculate LCM of 668,812
2 | 668, 812 |
2 | 334, 406 |
167, 203 |
∴ So the LCM of the given numbers is 2 x 2 x 167 x 203 = 135604
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/135604
Therefore, the GCF of Fractions 392/668,342/812 is 2/135604
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 668,812 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(668,812) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(668,812) x common factors =4 x 1 = 4
LCM(668,812) = ( 668 × 812 ) / 4
LCM(668,812) = 542416 / 4
LCM(668,812) = 135604
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 392,342?
The HCF of 392,342 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 392/668, 342/812?
Answer: GCF of Numerators as per given numbers 392/668, 342/812 is
GCF of Numerators i.e. for 392,342 is 2
LCM of denominators i.e. for 668,812 is 135604.
Thus, GCF of Fractions is 2/135604.Finally, GCF of Fractions for 392/668, 342/812 is 2/135604.