Use our free GCF of Fractions Calculator tool to compute the GCF of 207/698, 874/406 i.e 23/141694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 207/698, 874/406.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 207/698,874/406
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 207/698,874/406, numerators are 207,874
Denominators are 698,406
The GCF of 207,874 is 23 .
LCM of 698,406 is 141694.
The greatest common factor of 207/698,874/406 = [GCF of 207,874]/[LCM of 698,406]= 23/141694
Therefore, the GCF of 207/698,874/406 is 23/141694.
To find the highest common factor of 207,874, we have to find the factors of both numbers and list the highest common factor.
The factors of 207 are 1, 3, 9, 23, 69, 207
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The HCF of 207,874 is 23.
Lets's calculate GCF of 207,874
23 | 207, 874 |
9, 38 |
∴ So the GCF of the given numbers is 23 = 23
Now, list down the factors of 207
:1,3,9,23,69,207
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Greatest Common Factor
We found the factors 207,874 . The biggest common factor number is the GCF number.
So the greatest common factor 207,874 is 23.
Lets's calculate LCM of 698,406
2 | 698, 406 |
349, 203 |
∴ So the LCM of the given numbers is 2 x 349 x 203 = 141694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/141694
Therefore, the GCF of Fractions 207/698,874/406 is 23/141694
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 698,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(698,406) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(698,406) x common factors =2 x 1 = 2
LCM(698,406) = ( 698 × 406 ) / 2
LCM(698,406) = 283388 / 2
LCM(698,406) = 141694
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 207,874?
The HCF of 207,874 is 23
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 207/698, 874/406?
Answer: GCF of Numerators as per given numbers 207/698, 874/406 is
GCF of Numerators i.e. for 207,874 is 23
LCM of denominators i.e. for 698,406 is 141694.
Thus, GCF of Fractions is 23/141694.Finally, GCF of Fractions for 207/698, 874/406 is 23/141694.