Use our free GCF of Fractions Calculator tool to compute the GCF of 78/320, 49/870, 469/249 i.e 1/2310720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/320, 49/870, 469/249.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/320,49/870,469/249
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 78/320,49/870,469/249, numerators are 78,49,469
Denominators are 320,870,249
The GCF of 78,49,469 is 1 .
LCM of 320,870,249 is 2310720.
The greatest common factor of 78/320,49/870,469/249 = [GCF of 78,49,469]/[LCM of 320,870,249]= 1/2310720
Therefore, the GCF of 78/320,49/870,469/249 is 1/2310720.
To find the highest common factor of 78,49,469, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 49 are 1, 7, 49
The factors of 469 are 1, 7, 67, 469
The HCF of 78,49,469 is 1.
Lets's calculate GCF of 78,49,469
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 469
:1,7,67,469
Greatest Common Factor
We found the factors 78,49,469 . The biggest common factor number is the GCF number.
So the greatest common factor 78,49,469 is 1.
Lets's calculate LCM of 320,870,249
2 | 320, 870, 249 |
3 | 160, 435, 249 |
5 | 160, 145, 83 |
32, 29, 83 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 32 x 29 x 83 = 2310720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2310720
Therefore, the GCF of Fractions 78/320,49/870,469/249 is 1/2310720
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 320,870,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,870,249) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(320,870,249) x common factors =1 x 30 = 30
LCM(320,870,249) = ( 320 × 870 × 249 ) / 30
LCM(320,870,249) = 69321600 / 30
LCM(320,870,249) = 2310720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 78,49,469?
The HCF of 78,49,469 is 1
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 78/320, 49/870, 469/249?
Answer: GCF of Numerators as per given numbers 78/320, 49/870, 469/249 is
GCF of Numerators i.e. for 78,49,469 is 1
LCM of denominators i.e. for 320,870,249 is 2310720.
Thus, GCF of Fractions is 1/2310720.Finally, GCF of Fractions for 78/320, 49/870, 469/249 is 1/2310720.