Use our free GCF of Fractions Calculator tool to compute the GCF of 294/421, 214/275 i.e 2/115775 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/421, 214/275.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 294/421,214/275
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 294/421,214/275, numerators are 294,214
Denominators are 421,275
The GCF of 294,214 is 2 .
LCM of 421,275 is 115775.
The greatest common factor of 294/421,214/275 = [GCF of 294,214]/[LCM of 421,275]= 2/115775
Therefore, the GCF of 294/421,214/275 is 2/115775.
To find the highest common factor of 294,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The factors of 214 are 1, 2, 107, 214
The HCF of 294,214 is 2.
Lets's calculate GCF of 294,214
2 | 294, 214 |
147, 107 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 294,214 . The biggest common factor number is the GCF number.
So the greatest common factor 294,214 is 2.
Lets's calculate LCM of 421,275
Given numbers has no common factors except 1. So, there LCM is their product i.e 115775
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/115775
Therefore, the GCF of Fractions 294/421,214/275 is 2/115775
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 421,275 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,275) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,275) x common factors =1 x 1 = 1
LCM(421,275) = ( 421 × 275 ) / 1
LCM(421,275) = 115775 / 1
LCM(421,275) = 115775
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 294,214?
The HCF of 294,214 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 294/421, 214/275?
Answer: GCF of Numerators as per given numbers 294/421, 214/275 is
GCF of Numerators i.e. for 294,214 is 2
LCM of denominators i.e. for 421,275 is 115775.
Thus, GCF of Fractions is 2/115775.Finally, GCF of Fractions for 294/421, 214/275 is 2/115775.