Use our free GCF of Fractions Calculator tool to compute the GCF of 514/45, 564/132 i.e 2/1980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/45, 564/132.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 514/45,564/132
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 514/45,564/132, numerators are 514,564
Denominators are 45,132
The GCF of 514,564 is 2 .
LCM of 45,132 is 1980.
The greatest common factor of 514/45,564/132 = [GCF of 514,564]/[LCM of 45,132]= 2/1980
Therefore, the GCF of 514/45,564/132 is 2/1980.
To find the highest common factor of 514,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 514,564 is 2.
Lets's calculate GCF of 514,564
2 | 514, 564 |
257, 282 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 514,564 . The biggest common factor number is the GCF number.
So the greatest common factor 514,564 is 2.
Lets's calculate LCM of 45,132
3 | 45, 132 |
15, 44 |
∴ So the LCM of the given numbers is 3 x 15 x 44 = 1980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1980
Therefore, the GCF of Fractions 514/45,564/132 is 2/1980
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 45,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,132) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(45,132) x common factors =3 x 1 = 3
LCM(45,132) = ( 45 × 132 ) / 3
LCM(45,132) = 5940 / 3
LCM(45,132) = 1980
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 514,564?
The HCF of 514,564 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 514/45, 564/132?
Answer: GCF of Numerators as per given numbers 514/45, 564/132 is
GCF of Numerators i.e. for 514,564 is 2
LCM of denominators i.e. for 45,132 is 1980.
Thus, GCF of Fractions is 2/1980.Finally, GCF of Fractions for 514/45, 564/132 is 2/1980.