Use our free GCF of Fractions Calculator tool to compute the GCF of 564/577, 7314/294 i.e 6/169638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/577, 7314/294.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 564/577,7314/294
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 564/577,7314/294, numerators are 564,7314
Denominators are 577,294
The GCF of 564,7314 is 6 .
LCM of 577,294 is 169638.
The greatest common factor of 564/577,7314/294 = [GCF of 564,7314]/[LCM of 577,294]= 6/169638
Therefore, the GCF of 564/577,7314/294 is 6/169638.
To find the highest common factor of 564,7314, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 564,7314 is 6.
Lets's calculate GCF of 564,7314
2 | 564, 7314 |
3 | 282, 3657 |
94, 1219 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 564,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 564,7314 is 6.
Lets's calculate LCM of 577,294
Given numbers has no common factors except 1. So, there LCM is their product i.e 169638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/169638
Therefore, the GCF of Fractions 564/577,7314/294 is 6/169638
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 577,294 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(577,294) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(577,294) x common factors =1 x 1 = 1
LCM(577,294) = ( 577 × 294 ) / 1
LCM(577,294) = 169638 / 1
LCM(577,294) = 169638
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 564,7314?
The HCF of 564,7314 is 6
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 564/577, 7314/294?
Answer: GCF of Numerators as per given numbers 564/577, 7314/294 is
GCF of Numerators i.e. for 564,7314 is 6
LCM of denominators i.e. for 577,294 is 169638.
Thus, GCF of Fractions is 6/169638.Finally, GCF of Fractions for 564/577, 7314/294 is 6/169638.