Use our free GCF of Fractions Calculator tool to compute the GCF of 411/689, 237/678 i.e 3/467142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 411/689, 237/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 411/689,237/678
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 411/689,237/678, numerators are 411,237
Denominators are 689,678
The GCF of 411,237 is 3 .
LCM of 689,678 is 467142.
The greatest common factor of 411/689,237/678 = [GCF of 411,237]/[LCM of 689,678]= 3/467142
Therefore, the GCF of 411/689,237/678 is 3/467142.
To find the highest common factor of 411,237, we have to find the factors of both numbers and list the highest common factor.
The factors of 411 are 1, 3, 137, 411
The factors of 237 are 1, 3, 79, 237
The HCF of 411,237 is 3.
Lets's calculate GCF of 411,237
3 | 411, 237 |
137, 79 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 411
:1,3,137,411
Now, list down the factors of 237
:1,3,79,237
Greatest Common Factor
We found the factors 411,237 . The biggest common factor number is the GCF number.
So the greatest common factor 411,237 is 3.
Lets's calculate LCM of 689,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 467142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/467142
Therefore, the GCF of Fractions 411/689,237/678 is 3/467142
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 689,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,678) x common factors =1 x 1 = 1
LCM(689,678) = ( 689 × 678 ) / 1
LCM(689,678) = 467142 / 1
LCM(689,678) = 467142
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 411,237?
The HCF of 411,237 is 3
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 411/689, 237/678?
Answer: GCF of Numerators as per given numbers 411/689, 237/678 is
GCF of Numerators i.e. for 411,237 is 3
LCM of denominators i.e. for 689,678 is 467142.
Thus, GCF of Fractions is 3/467142.Finally, GCF of Fractions for 411/689, 237/678 is 3/467142.