Use our free GCF of Fractions Calculator tool to compute the GCF of 684/627, 270/173 i.e 18/108471 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/627, 270/173.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 684/627,270/173
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 684/627,270/173, numerators are 684,270
Denominators are 627,173
The GCF of 684,270 is 18 .
LCM of 627,173 is 108471.
The greatest common factor of 684/627,270/173 = [GCF of 684,270]/[LCM of 627,173]= 18/108471
Therefore, the GCF of 684/627,270/173 is 18/108471.
To find the highest common factor of 684,270, we have to find the factors of both numbers and list the highest common factor.
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 684,270 is 18.
Lets's calculate GCF of 684,270
2 | 684, 270 |
3 | 342, 135 |
3 | 114, 45 |
38, 15 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Greatest Common Factor
We found the factors 684,270 . The biggest common factor number is the GCF number.
So the greatest common factor 684,270 is 18.
Lets's calculate LCM of 627,173
Given numbers has no common factors except 1. So, there LCM is their product i.e 108471
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/108471
Therefore, the GCF of Fractions 684/627,270/173 is 18/108471
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 627,173 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(627,173) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(627,173) x common factors =1 x 1 = 1
LCM(627,173) = ( 627 × 173 ) / 1
LCM(627,173) = 108471 / 1
LCM(627,173) = 108471
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 684,270?
The HCF of 684,270 is 18
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 684/627, 270/173?
Answer: GCF of Numerators as per given numbers 684/627, 270/173 is
GCF of Numerators i.e. for 684,270 is 18
LCM of denominators i.e. for 627,173 is 108471.
Thus, GCF of Fractions is 18/108471.Finally, GCF of Fractions for 684/627, 270/173 is 18/108471.