Use our free GCF of Fractions Calculator tool to compute the GCF of 980/540, 210/987 i.e 70/177660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 980/540, 210/987.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 980/540,210/987
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 980/540,210/987, numerators are 980,210
Denominators are 540,987
The GCF of 980,210 is 70 .
LCM of 540,987 is 177660.
The greatest common factor of 980/540,210/987 = [GCF of 980,210]/[LCM of 540,987]= 70/177660
Therefore, the GCF of 980/540,210/987 is 70/177660.
To find the highest common factor of 980,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 980,210 is 70.
Lets's calculate GCF of 980,210
2 | 980, 210 |
5 | 490, 105 |
7 | 98, 21 |
14, 3 |
∴ So the GCF of the given numbers is 2 x 5 x 7 = 70
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 980,210 . The biggest common factor number is the GCF number.
So the greatest common factor 980,210 is 70.
Lets's calculate LCM of 540,987
3 | 540, 987 |
180, 329 |
∴ So the LCM of the given numbers is 3 x 180 x 329 = 177660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/177660
Therefore, the GCF of Fractions 980/540,210/987 is 70/177660
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 540,987 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,987) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(540,987) x common factors =3 x 1 = 3
LCM(540,987) = ( 540 × 987 ) / 3
LCM(540,987) = 532980 / 3
LCM(540,987) = 177660
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 980,210?
The HCF of 980,210 is 70
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 980/540, 210/987?
Answer: GCF of Numerators as per given numbers 980/540, 210/987 is
GCF of Numerators i.e. for 980,210 is 70
LCM of denominators i.e. for 540,987 is 177660.
Thus, GCF of Fractions is 70/177660.Finally, GCF of Fractions for 980/540, 210/987 is 70/177660.