Use our free GCF of Fractions Calculator tool to compute the GCF of 87/279, 48/620, 519/954 i.e 3/295740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/279, 48/620, 519/954.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 87/279,48/620,519/954
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 87/279,48/620,519/954, numerators are 87,48,519
Denominators are 279,620,954
The GCF of 87,48,519 is 3 .
LCM of 279,620,954 is 295740.
The greatest common factor of 87/279,48/620,519/954 = [GCF of 87,48,519]/[LCM of 279,620,954]= 3/295740
Therefore, the GCF of 87/279,48/620,519/954 is 3/295740.
To find the highest common factor of 87,48,519, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 519 are 1, 3, 173, 519
The HCF of 87,48,519 is 3.
Lets's calculate GCF of 87,48,519
3 | 87, 48, 519 |
29, 16, 173 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 519
:1,3,173,519
Greatest Common Factor
We found the factors 87,48,519 . The biggest common factor number is the GCF number.
So the greatest common factor 87,48,519 is 3.
Lets's calculate LCM of 279,620,954
2 | 279, 620, 954 |
3 | 279, 310, 477 |
3 | 93, 310, 159 |
31 | 31, 310, 53 |
1, 10, 53 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 31 x 1 x 10 x 53 = 295740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/295740
Therefore, the GCF of Fractions 87/279,48/620,519/954 is 3/295740
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 279,620,954 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(279,620,954) = 1
common factors(in case of two or more numbers have common factors) = 558
GCF(279,620,954) x common factors =1 x 558 = 558
LCM(279,620,954) = ( 279 × 620 × 954 ) / 558
LCM(279,620,954) = 165022920 / 558
LCM(279,620,954) = 295740
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 87,48,519?
The HCF of 87,48,519 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 87/279, 48/620, 519/954?
Answer: GCF of Numerators as per given numbers 87/279, 48/620, 519/954 is
GCF of Numerators i.e. for 87,48,519 is 3
LCM of denominators i.e. for 279,620,954 is 295740.
Thus, GCF of Fractions is 3/295740.Finally, GCF of Fractions for 87/279, 48/620, 519/954 is 3/295740.