Use our free GCF of Fractions Calculator tool to compute the GCF of 414/108, 178/241 i.e 2/26028 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/108, 178/241.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 414/108,178/241
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 414/108,178/241, numerators are 414,178
Denominators are 108,241
The GCF of 414,178 is 2 .
LCM of 108,241 is 26028.
The greatest common factor of 414/108,178/241 = [GCF of 414,178]/[LCM of 108,241]= 2/26028
Therefore, the GCF of 414/108,178/241 is 2/26028.
To find the highest common factor of 414,178, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 178 are 1, 2, 89, 178
The HCF of 414,178 is 2.
Lets's calculate GCF of 414,178
2 | 414, 178 |
207, 89 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 178
:1,2,89,178
Greatest Common Factor
We found the factors 414,178 . The biggest common factor number is the GCF number.
So the greatest common factor 414,178 is 2.
Lets's calculate LCM of 108,241
Given numbers has no common factors except 1. So, there LCM is their product i.e 26028
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/26028
Therefore, the GCF of Fractions 414/108,178/241 is 2/26028
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 108,241 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(108,241) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(108,241) x common factors =1 x 1 = 1
LCM(108,241) = ( 108 × 241 ) / 1
LCM(108,241) = 26028 / 1
LCM(108,241) = 26028
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 414,178?
The HCF of 414,178 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 414/108, 178/241?
Answer: GCF of Numerators as per given numbers 414/108, 178/241 is
GCF of Numerators i.e. for 414,178 is 2
LCM of denominators i.e. for 108,241 is 26028.
Thus, GCF of Fractions is 2/26028.Finally, GCF of Fractions for 414/108, 178/241 is 2/26028.