Use our free GCF of Fractions Calculator tool to compute the GCF of 270/757, 570/678 i.e 30/513246 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/757, 570/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 270/757,570/678
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 270/757,570/678, numerators are 270,570
Denominators are 757,678
The GCF of 270,570 is 30 .
LCM of 757,678 is 513246.
The greatest common factor of 270/757,570/678 = [GCF of 270,570]/[LCM of 757,678]= 30/513246
Therefore, the GCF of 270/757,570/678 is 30/513246.
To find the highest common factor of 270,570, we have to find the factors of both numbers and list the highest common factor.
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The factors of 570 are 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
The HCF of 270,570 is 30.
Lets's calculate GCF of 270,570
2 | 270, 570 |
3 | 135, 285 |
5 | 45, 95 |
9, 19 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Now, list down the factors of 570
:1,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570
Greatest Common Factor
We found the factors 270,570 . The biggest common factor number is the GCF number.
So the greatest common factor 270,570 is 30.
Lets's calculate LCM of 757,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 513246
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/513246
Therefore, the GCF of Fractions 270/757,570/678 is 30/513246
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 757,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(757,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(757,678) x common factors =1 x 1 = 1
LCM(757,678) = ( 757 × 678 ) / 1
LCM(757,678) = 513246 / 1
LCM(757,678) = 513246
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 270,570?
The HCF of 270,570 is 30
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 270/757, 570/678?
Answer: GCF of Numerators as per given numbers 270/757, 570/678 is
GCF of Numerators i.e. for 270,570 is 30
LCM of denominators i.e. for 757,678 is 513246.
Thus, GCF of Fractions is 30/513246.Finally, GCF of Fractions for 270/757, 570/678 is 30/513246.