Use our free GCF of Fractions Calculator tool to compute the GCF of 278/466, 508/684 i.e 2/159372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/466, 508/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 278/466,508/684
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 278/466,508/684, numerators are 278,508
Denominators are 466,684
The GCF of 278,508 is 2 .
LCM of 466,684 is 159372.
The greatest common factor of 278/466,508/684 = [GCF of 278,508]/[LCM of 466,684]= 2/159372
Therefore, the GCF of 278/466,508/684 is 2/159372.
To find the highest common factor of 278,508, we have to find the factors of both numbers and list the highest common factor.
The factors of 278 are 1, 2, 139, 278
The factors of 508 are 1, 2, 4, 127, 254, 508
The HCF of 278,508 is 2.
Lets's calculate GCF of 278,508
2 | 278, 508 |
139, 254 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 508
:1,2,4,127,254,508
Greatest Common Factor
We found the factors 278,508 . The biggest common factor number is the GCF number.
So the greatest common factor 278,508 is 2.
Lets's calculate LCM of 466,684
2 | 466, 684 |
233, 342 |
∴ So the LCM of the given numbers is 2 x 233 x 342 = 159372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/159372
Therefore, the GCF of Fractions 278/466,508/684 is 2/159372
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 466,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(466,684) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(466,684) x common factors =2 x 1 = 2
LCM(466,684) = ( 466 × 684 ) / 2
LCM(466,684) = 318744 / 2
LCM(466,684) = 159372
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 278,508?
The HCF of 278,508 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 278/466, 508/684?
Answer: GCF of Numerators as per given numbers 278/466, 508/684 is
GCF of Numerators i.e. for 278,508 is 2
LCM of denominators i.e. for 466,684 is 159372.
Thus, GCF of Fractions is 2/159372.Finally, GCF of Fractions for 278/466, 508/684 is 2/159372.