Use our free GCF of Fractions Calculator tool to compute the GCF of 67/414, 62/268, 666/727 i.e 1/40331052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/414, 62/268, 666/727.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 67/414,62/268,666/727
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 67/414,62/268,666/727, numerators are 67,62,666
Denominators are 414,268,727
The GCF of 67,62,666 is 1 .
LCM of 414,268,727 is 40331052.
The greatest common factor of 67/414,62/268,666/727 = [GCF of 67,62,666]/[LCM of 414,268,727]= 1/40331052
Therefore, the GCF of 67/414,62/268,666/727 is 1/40331052.
To find the highest common factor of 67,62,666, we have to find the factors of both numbers and list the highest common factor.
The factors of 67 are 1, 67
The factors of 62 are 1, 2, 31, 62
The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The HCF of 67,62,666 is 1.
Lets's calculate GCF of 67,62,666
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 67
:1,67
Now, list down the factors of 62
:1,2,31,62
Now, list down the factors of 666
:1,2,3,6,9,18,37,74,111,222,333,666
Greatest Common Factor
We found the factors 67,62,666 . The biggest common factor number is the GCF number.
So the greatest common factor 67,62,666 is 1.
Lets's calculate LCM of 414,268,727
2 | 414, 268, 727 |
207, 134, 727 |
∴ So the LCM of the given numbers is 2 x 207 x 134 x 727 = 40331052
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40331052
Therefore, the GCF of Fractions 67/414,62/268,666/727 is 1/40331052
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 414,268,727 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,268,727) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(414,268,727) x common factors =1 x 2 = 2
LCM(414,268,727) = ( 414 × 268 × 727 ) / 2
LCM(414,268,727) = 80662104 / 2
LCM(414,268,727) = 40331052
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 67,62,666?
The HCF of 67,62,666 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 67/414, 62/268, 666/727?
Answer: GCF of Numerators as per given numbers 67/414, 62/268, 666/727 is
GCF of Numerators i.e. for 67,62,666 is 1
LCM of denominators i.e. for 414,268,727 is 40331052.
Thus, GCF of Fractions is 1/40331052.Finally, GCF of Fractions for 67/414, 62/268, 666/727 is 1/40331052.