Use our free GCF of Fractions Calculator tool to compute the GCF of 267/217, 564/530 i.e 3/115010 easily. The following is the detailed procedure to determine the greatest common factor of fractions 267/217, 564/530.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 267/217,564/530
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 267/217,564/530, numerators are 267,564
Denominators are 217,530
The GCF of 267,564 is 3 .
LCM of 217,530 is 115010.
The greatest common factor of 267/217,564/530 = [GCF of 267,564]/[LCM of 217,530]= 3/115010
Therefore, the GCF of 267/217,564/530 is 3/115010.
To find the highest common factor of 267,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 267 are 1, 3, 89, 267
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 267,564 is 3.
Lets's calculate GCF of 267,564
3 | 267, 564 |
89, 188 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 267
:1,3,89,267
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 267,564 . The biggest common factor number is the GCF number.
So the greatest common factor 267,564 is 3.
Lets's calculate LCM of 217,530
Given numbers has no common factors except 1. So, there LCM is their product i.e 115010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/115010
Therefore, the GCF of Fractions 267/217,564/530 is 3/115010
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 217,530 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,530) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,530) x common factors =1 x 1 = 1
LCM(217,530) = ( 217 × 530 ) / 1
LCM(217,530) = 115010 / 1
LCM(217,530) = 115010
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 267,564?
The HCF of 267,564 is 3
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 267/217, 564/530?
Answer: GCF of Numerators as per given numbers 267/217, 564/530 is
GCF of Numerators i.e. for 267,564 is 3
LCM of denominators i.e. for 217,530 is 115010.
Thus, GCF of Fractions is 3/115010.Finally, GCF of Fractions for 267/217, 564/530 is 3/115010.