Use our free GCF of Fractions Calculator tool to compute the GCF of 69/242, 61/3430 i.e 1/415030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/242, 61/3430.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/242,61/3430
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 69/242,61/3430, numerators are 69,61
Denominators are 242,3430
The GCF of 69,61 is 1 .
LCM of 242,3430 is 415030.
The greatest common factor of 69/242,61/3430 = [GCF of 69,61]/[LCM of 242,3430]= 1/415030
Therefore, the GCF of 69/242,61/3430 is 1/415030.
To find the highest common factor of 69,61, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 61 are 1, 61
The HCF of 69,61 is 1.
Lets's calculate GCF of 69,61
∴ So GCF of numbers is 1 because of no common factors present between them.
Lets's calculate LCM of 242,3430
2 | 242, 3430 |
121, 1715 |
∴ So the LCM of the given numbers is 2 x 121 x 1715 = 415030
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/415030
Therefore, the GCF of Fractions 69/242,61/3430 is 1/415030
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 242,3430 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(242,3430) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(242,3430) x common factors =2 x 1 = 2
LCM(242,3430) = ( 242 × 3430 ) / 2
LCM(242,3430) = 830060 / 2
LCM(242,3430) = 415030
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 69,61?
The HCF of 69,61 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 69/242, 61/3430?
Answer: GCF of Numerators as per given numbers 69/242, 61/3430 is
GCF of Numerators i.e. for 69,61 is 1
LCM of denominators i.e. for 242,3430 is 415030.
Thus, GCF of Fractions is 1/415030.Finally, GCF of Fractions for 69/242, 61/3430 is 1/415030.