Use our free GCF of Fractions Calculator tool to compute the GCF of 209/660, 338/178 i.e 1/58740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/660, 338/178.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 209/660,338/178
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 209/660,338/178, numerators are 209,338
Denominators are 660,178
The GCF of 209,338 is 1 .
LCM of 660,178 is 58740.
The greatest common factor of 209/660,338/178 = [GCF of 209,338]/[LCM of 660,178]= 1/58740
Therefore, the GCF of 209/660,338/178 is 1/58740.
To find the highest common factor of 209,338, we have to find the factors of both numbers and list the highest common factor.
The factors of 209 are 1, 11, 19, 209
The factors of 338 are 1, 2, 13, 26, 169, 338
The HCF of 209,338 is 1.
Lets's calculate GCF of 209,338
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 209
:1,11,19,209
Now, list down the factors of 338
:1,2,13,26,169,338
Greatest Common Factor
We found the factors 209,338 . The biggest common factor number is the GCF number.
So the greatest common factor 209,338 is 1.
Lets's calculate LCM of 660,178
2 | 660, 178 |
330, 89 |
∴ So the LCM of the given numbers is 2 x 330 x 89 = 58740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/58740
Therefore, the GCF of Fractions 209/660,338/178 is 1/58740
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 660,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(660,178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(660,178) x common factors =2 x 1 = 2
LCM(660,178) = ( 660 × 178 ) / 2
LCM(660,178) = 117480 / 2
LCM(660,178) = 58740
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 209,338?
The HCF of 209,338 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 209/660, 338/178?
Answer: GCF of Numerators as per given numbers 209/660, 338/178 is
GCF of Numerators i.e. for 209,338 is 1
LCM of denominators i.e. for 660,178 is 58740.
Thus, GCF of Fractions is 1/58740.Finally, GCF of Fractions for 209/660, 338/178 is 1/58740.