Use our free GCF of Fractions Calculator tool to compute the GCF of 861/430, 280/588 i.e 7/126420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 861/430, 280/588.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 861/430,280/588
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 861/430,280/588, numerators are 861,280
Denominators are 430,588
The GCF of 861,280 is 7 .
LCM of 430,588 is 126420.
The greatest common factor of 861/430,280/588 = [GCF of 861,280]/[LCM of 430,588]= 7/126420
Therefore, the GCF of 861/430,280/588 is 7/126420.
To find the highest common factor of 861,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 861,280 is 7.
Lets's calculate GCF of 861,280
7 | 861, 280 |
123, 40 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 861,280 . The biggest common factor number is the GCF number.
So the greatest common factor 861,280 is 7.
Lets's calculate LCM of 430,588
2 | 430, 588 |
215, 294 |
∴ So the LCM of the given numbers is 2 x 215 x 294 = 126420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/126420
Therefore, the GCF of Fractions 861/430,280/588 is 7/126420
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 430,588 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(430,588) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(430,588) x common factors =2 x 1 = 2
LCM(430,588) = ( 430 × 588 ) / 2
LCM(430,588) = 252840 / 2
LCM(430,588) = 126420
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 861,280?
The HCF of 861,280 is 7
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 861/430, 280/588?
Answer: GCF of Numerators as per given numbers 861/430, 280/588 is
GCF of Numerators i.e. for 861,280 is 7
LCM of denominators i.e. for 430,588 is 126420.
Thus, GCF of Fractions is 7/126420.Finally, GCF of Fractions for 861/430, 280/588 is 7/126420.