Use our free GCF of Fractions Calculator tool to compute the GCF of 982/217, 688/270 i.e 2/58590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 982/217, 688/270.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 982/217,688/270
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 982/217,688/270, numerators are 982,688
Denominators are 217,270
The GCF of 982,688 is 2 .
LCM of 217,270 is 58590.
The greatest common factor of 982/217,688/270 = [GCF of 982,688]/[LCM of 217,270]= 2/58590
Therefore, the GCF of 982/217,688/270 is 2/58590.
To find the highest common factor of 982,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 982 are 1, 2, 491, 982
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 982,688 is 2.
Lets's calculate GCF of 982,688
2 | 982, 688 |
491, 344 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 982
:1,2,491,982
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 982,688 . The biggest common factor number is the GCF number.
So the greatest common factor 982,688 is 2.
Lets's calculate LCM of 217,270
Given numbers has no common factors except 1. So, there LCM is their product i.e 58590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/58590
Therefore, the GCF of Fractions 982/217,688/270 is 2/58590
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 217,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,270) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,270) x common factors =1 x 1 = 1
LCM(217,270) = ( 217 × 270 ) / 1
LCM(217,270) = 58590 / 1
LCM(217,270) = 58590
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 982,688?
The HCF of 982,688 is 2
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 982/217, 688/270?
Answer: GCF of Numerators as per given numbers 982/217, 688/270 is
GCF of Numerators i.e. for 982,688 is 2
LCM of denominators i.e. for 217,270 is 58590.
Thus, GCF of Fractions is 2/58590.Finally, GCF of Fractions for 982/217, 688/270 is 2/58590.