Use our free GCF of Fractions Calculator tool to compute the GCF of 218/171, 767/428 i.e 1/73188 easily. The following is the detailed procedure to determine the greatest common factor of fractions 218/171, 767/428.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 218/171,767/428
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 218/171,767/428, numerators are 218,767
Denominators are 171,428
The GCF of 218,767 is 1 .
LCM of 171,428 is 73188.
The greatest common factor of 218/171,767/428 = [GCF of 218,767]/[LCM of 171,428]= 1/73188
Therefore, the GCF of 218/171,767/428 is 1/73188.
To find the highest common factor of 218,767, we have to find the factors of both numbers and list the highest common factor.
The factors of 218 are 1, 2, 109, 218
The factors of 767 are 1, 13, 59, 767
The HCF of 218,767 is 1.
Lets's calculate GCF of 218,767
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 218
:1,2,109,218
Now, list down the factors of 767
:1,13,59,767
Greatest Common Factor
We found the factors 218,767 . The biggest common factor number is the GCF number.
So the greatest common factor 218,767 is 1.
Lets's calculate LCM of 171,428
Given numbers has no common factors except 1. So, there LCM is their product i.e 73188
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/73188
Therefore, the GCF of Fractions 218/171,767/428 is 1/73188
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 171,428 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(171,428) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(171,428) x common factors =1 x 1 = 1
LCM(171,428) = ( 171 × 428 ) / 1
LCM(171,428) = 73188 / 1
LCM(171,428) = 73188
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 218,767?
The HCF of 218,767 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 218/171, 767/428?
Answer: GCF of Numerators as per given numbers 218/171, 767/428 is
GCF of Numerators i.e. for 218,767 is 1
LCM of denominators i.e. for 171,428 is 73188.
Thus, GCF of Fractions is 1/73188.Finally, GCF of Fractions for 218/171, 767/428 is 1/73188.