Use our free GCF of Fractions Calculator tool to compute the GCF of 30/91, 70/61, 346/176 i.e 2/976976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/91, 70/61, 346/176.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/91,70/61,346/176
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 30/91,70/61,346/176, numerators are 30,70,346
Denominators are 91,61,176
The GCF of 30,70,346 is 2 .
LCM of 91,61,176 is 976976.
The greatest common factor of 30/91,70/61,346/176 = [GCF of 30,70,346]/[LCM of 91,61,176]= 2/976976
Therefore, the GCF of 30/91,70/61,346/176 is 2/976976.
To find the highest common factor of 30,70,346, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 346 are 1, 2, 173, 346
The HCF of 30,70,346 is 2.
Lets's calculate GCF of 30,70,346
2 | 30, 70, 346 |
15, 35, 173 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 346
:1,2,173,346
Greatest Common Factor
We found the factors 30,70,346 . The biggest common factor number is the GCF number.
So the greatest common factor 30,70,346 is 2.
Lets's calculate LCM of 91,61,176
Given numbers has no common factors except 1. So, there LCM is their product i.e 976976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/976976
Therefore, the GCF of Fractions 30/91,70/61,346/176 is 2/976976
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 91,61,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(91,61,176) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(91,61,176) x common factors =1 x 1 = 1
LCM(91,61,176) = ( 91 × 61 × 176 ) / 1
LCM(91,61,176) = 976976 / 1
LCM(91,61,176) = 976976
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,70,346?
The HCF of 30,70,346 is 2
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 30/91, 70/61, 346/176?
Answer: GCF of Numerators as per given numbers 30/91, 70/61, 346/176 is
GCF of Numerators i.e. for 30,70,346 is 2
LCM of denominators i.e. for 91,61,176 is 976976.
Thus, GCF of Fractions is 2/976976.Finally, GCF of Fractions for 30/91, 70/61, 346/176 is 2/976976.