Use our free GCF of Fractions Calculator tool to compute the GCF of 306/564, 775/546 i.e 1/51324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/564, 775/546.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 306/564,775/546
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 306/564,775/546, numerators are 306,775
Denominators are 564,546
The GCF of 306,775 is 1 .
LCM of 564,546 is 51324.
The greatest common factor of 306/564,775/546 = [GCF of 306,775]/[LCM of 564,546]= 1/51324
Therefore, the GCF of 306/564,775/546 is 1/51324.
To find the highest common factor of 306,775, we have to find the factors of both numbers and list the highest common factor.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 775 are 1, 5, 25, 31, 155, 775
The HCF of 306,775 is 1.
Lets's calculate GCF of 306,775
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 775
:1,5,25,31,155,775
Greatest Common Factor
We found the factors 306,775 . The biggest common factor number is the GCF number.
So the greatest common factor 306,775 is 1.
Lets's calculate LCM of 564,546
2 | 564, 546 |
3 | 282, 273 |
94, 91 |
∴ So the LCM of the given numbers is 2 x 3 x 94 x 91 = 51324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51324
Therefore, the GCF of Fractions 306/564,775/546 is 1/51324
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 564,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,546) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(564,546) x common factors =6 x 1 = 6
LCM(564,546) = ( 564 × 546 ) / 6
LCM(564,546) = 307944 / 6
LCM(564,546) = 51324
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 306,775?
The HCF of 306,775 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 306/564, 775/546?
Answer: GCF of Numerators as per given numbers 306/564, 775/546 is
GCF of Numerators i.e. for 306,775 is 1
LCM of denominators i.e. for 564,546 is 51324.
Thus, GCF of Fractions is 1/51324.Finally, GCF of Fractions for 306/564, 775/546 is 1/51324.