Use our free GCF of Fractions Calculator tool to compute the GCF of 865/274, 130/324 i.e 5/44388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 865/274, 130/324.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 865/274,130/324
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 865/274,130/324, numerators are 865,130
Denominators are 274,324
The GCF of 865,130 is 5 .
LCM of 274,324 is 44388.
The greatest common factor of 865/274,130/324 = [GCF of 865,130]/[LCM of 274,324]= 5/44388
Therefore, the GCF of 865/274,130/324 is 5/44388.
To find the highest common factor of 865,130, we have to find the factors of both numbers and list the highest common factor.
The factors of 865 are 1, 5, 173, 865
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130
The HCF of 865,130 is 5.
Lets's calculate GCF of 865,130
5 | 865, 130 |
173, 26 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 865
:1,5,173,865
Now, list down the factors of 130
:1,2,5,10,13,26,65,130
Greatest Common Factor
We found the factors 865,130 . The biggest common factor number is the GCF number.
So the greatest common factor 865,130 is 5.
Lets's calculate LCM of 274,324
2 | 274, 324 |
137, 162 |
∴ So the LCM of the given numbers is 2 x 137 x 162 = 44388
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/44388
Therefore, the GCF of Fractions 865/274,130/324 is 5/44388
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 274,324 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,324) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,324) x common factors =2 x 1 = 2
LCM(274,324) = ( 274 × 324 ) / 2
LCM(274,324) = 88776 / 2
LCM(274,324) = 44388
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 865,130?
The HCF of 865,130 is 5
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 865/274, 130/324?
Answer: GCF of Numerators as per given numbers 865/274, 130/324 is
GCF of Numerators i.e. for 865,130 is 5
LCM of denominators i.e. for 274,324 is 44388.
Thus, GCF of Fractions is 5/44388.Finally, GCF of Fractions for 865/274, 130/324 is 5/44388.