Use our free GCF of Fractions Calculator tool to compute the GCF of 497/540, 1982/1412 i.e 1/190620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 497/540, 1982/1412.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 497/540,1982/1412
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 497/540,1982/1412, numerators are 497,1982
Denominators are 540,1412
The GCF of 497,1982 is 1 .
LCM of 540,1412 is 190620.
The greatest common factor of 497/540,1982/1412 = [GCF of 497,1982]/[LCM of 540,1412]= 1/190620
Therefore, the GCF of 497/540,1982/1412 is 1/190620.
To find the highest common factor of 497,1982, we have to find the factors of both numbers and list the highest common factor.
The factors of 497 are 1, 7, 71, 497
The factors of 1982 are 1, 2, 991, 1982
The HCF of 497,1982 is 1.
Lets's calculate GCF of 497,1982
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 497
:1,7,71,497
Now, list down the factors of 1982
:1,2,991,1982
Greatest Common Factor
We found the factors 497,1982 . The biggest common factor number is the GCF number.
So the greatest common factor 497,1982 is 1.
Lets's calculate LCM of 540,1412
2 | 540, 1412 |
2 | 270, 706 |
135, 353 |
∴ So the LCM of the given numbers is 2 x 2 x 135 x 353 = 190620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/190620
Therefore, the GCF of Fractions 497/540,1982/1412 is 1/190620
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 540,1412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,1412) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(540,1412) x common factors =4 x 1 = 4
LCM(540,1412) = ( 540 × 1412 ) / 4
LCM(540,1412) = 762480 / 4
LCM(540,1412) = 190620
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 497,1982?
The HCF of 497,1982 is 1
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 497/540, 1982/1412?
Answer: GCF of Numerators as per given numbers 497/540, 1982/1412 is
GCF of Numerators i.e. for 497,1982 is 1
LCM of denominators i.e. for 540,1412 is 190620.
Thus, GCF of Fractions is 1/190620.Finally, GCF of Fractions for 497/540, 1982/1412 is 1/190620.