Use our free GCF of Fractions Calculator tool to compute the GCF of 242/280, 137/184 i.e 1/6440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 242/280, 137/184.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 242/280,137/184
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 242/280,137/184, numerators are 242,137
Denominators are 280,184
The GCF of 242,137 is 1 .
LCM of 280,184 is 6440.
The greatest common factor of 242/280,137/184 = [GCF of 242,137]/[LCM of 280,184]= 1/6440
Therefore, the GCF of 242/280,137/184 is 1/6440.
To find the highest common factor of 242,137, we have to find the factors of both numbers and list the highest common factor.
The factors of 242 are 1, 2, 11, 22, 121, 242
The factors of 137 are 1, 137
The HCF of 242,137 is 1.
Lets's calculate GCF of 242,137
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 242
:1,2,11,22,121,242
Now, list down the factors of 137
:1,137
Greatest Common Factor
We found the factors 242,137 . The biggest common factor number is the GCF number.
So the greatest common factor 242,137 is 1.
Lets's calculate LCM of 280,184
2 | 280, 184 |
2 | 140, 92 |
2 | 70, 46 |
35, 23 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 35 x 23 = 6440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6440
Therefore, the GCF of Fractions 242/280,137/184 is 1/6440
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 280,184 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(280,184) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(280,184) x common factors =8 x 1 = 8
LCM(280,184) = ( 280 × 184 ) / 8
LCM(280,184) = 51520 / 8
LCM(280,184) = 6440
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 242,137?
The HCF of 242,137 is 1
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 242/280, 137/184?
Answer: GCF of Numerators as per given numbers 242/280, 137/184 is
GCF of Numerators i.e. for 242,137 is 1
LCM of denominators i.e. for 280,184 is 6440.
Thus, GCF of Fractions is 1/6440.Finally, GCF of Fractions for 242/280, 137/184 is 1/6440.