Use our free GCF of Fractions Calculator tool to compute the GCF of 438/660, 698/208 i.e 2/34320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 438/660, 698/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 438/660,698/208
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 438/660,698/208, numerators are 438,698
Denominators are 660,208
The GCF of 438,698 is 2 .
LCM of 660,208 is 34320.
The greatest common factor of 438/660,698/208 = [GCF of 438,698]/[LCM of 660,208]= 2/34320
Therefore, the GCF of 438/660,698/208 is 2/34320.
To find the highest common factor of 438,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The factors of 698 are 1, 2, 349, 698
The HCF of 438,698 is 2.
Lets's calculate GCF of 438,698
2 | 438, 698 |
219, 349 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 438,698 . The biggest common factor number is the GCF number.
So the greatest common factor 438,698 is 2.
Lets's calculate LCM of 660,208
2 | 660, 208 |
2 | 330, 104 |
165, 52 |
∴ So the LCM of the given numbers is 2 x 2 x 165 x 52 = 34320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/34320
Therefore, the GCF of Fractions 438/660,698/208 is 2/34320
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 660,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(660,208) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(660,208) x common factors =4 x 1 = 4
LCM(660,208) = ( 660 × 208 ) / 4
LCM(660,208) = 137280 / 4
LCM(660,208) = 34320
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 438,698?
The HCF of 438,698 is 2
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 438/660, 698/208?
Answer: GCF of Numerators as per given numbers 438/660, 698/208 is
GCF of Numerators i.e. for 438,698 is 2
LCM of denominators i.e. for 660,208 is 34320.
Thus, GCF of Fractions is 2/34320.Finally, GCF of Fractions for 438/660, 698/208 is 2/34320.