Use our free GCF of Fractions Calculator tool to compute the GCF of 245/570, 686/760 i.e 49/2280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 245/570, 686/760.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 245/570,686/760
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 245/570,686/760, numerators are 245,686
Denominators are 570,760
The GCF of 245,686 is 49 .
LCM of 570,760 is 2280.
The greatest common factor of 245/570,686/760 = [GCF of 245,686]/[LCM of 570,760]= 49/2280
Therefore, the GCF of 245/570,686/760 is 49/2280.
To find the highest common factor of 245,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 245 are 1, 5, 7, 35, 49, 245
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 245,686 is 49.
Lets's calculate GCF of 245,686
7 | 245, 686 |
7 | 35, 98 |
5, 14 |
∴ So the GCF of the given numbers is 7 x 7 = 49
Now, list down the factors of 245
:1,5,7,35,49,245
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 245,686 . The biggest common factor number is the GCF number.
So the greatest common factor 245,686 is 49.
Lets's calculate LCM of 570,760
2 | 570, 760 |
5 | 285, 380 |
19 | 57, 76 |
3, 4 |
∴ So the LCM of the given numbers is 2 x 5 x 19 x 3 x 4 = 2280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 49/2280
Therefore, the GCF of Fractions 245/570,686/760 is 49/2280
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 570,760 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(570,760) = 190
common factors(in case of two or more numbers have common factors) = 1
GCF(570,760) x common factors =190 x 1 = 190
LCM(570,760) = ( 570 × 760 ) / 190
LCM(570,760) = 433200 / 190
LCM(570,760) = 2280
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 245,686?
The HCF of 245,686 is 49
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 245/570, 686/760?
Answer: GCF of Numerators as per given numbers 245/570, 686/760 is
GCF of Numerators i.e. for 245,686 is 49
LCM of denominators i.e. for 570,760 is 2280.
Thus, GCF of Fractions is 49/2280.Finally, GCF of Fractions for 245/570, 686/760 is 49/2280.