Use our free GCF of Fractions Calculator tool to compute the GCF of 306/370, 120/377 i.e 6/139490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/370, 120/377.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 306/370,120/377
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 306/370,120/377, numerators are 306,120
Denominators are 370,377
The GCF of 306,120 is 6 .
LCM of 370,377 is 139490.
The greatest common factor of 306/370,120/377 = [GCF of 306,120]/[LCM of 370,377]= 6/139490
Therefore, the GCF of 306/370,120/377 is 6/139490.
To find the highest common factor of 306,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 306,120 is 6.
Lets's calculate GCF of 306,120
2 | 306, 120 |
3 | 153, 60 |
51, 20 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 306,120 . The biggest common factor number is the GCF number.
So the greatest common factor 306,120 is 6.
Lets's calculate LCM of 370,377
Given numbers has no common factors except 1. So, there LCM is their product i.e 139490
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/139490
Therefore, the GCF of Fractions 306/370,120/377 is 6/139490
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 370,377 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(370,377) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(370,377) x common factors =1 x 1 = 1
LCM(370,377) = ( 370 × 377 ) / 1
LCM(370,377) = 139490 / 1
LCM(370,377) = 139490
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 306,120?
The HCF of 306,120 is 6
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 306/370, 120/377?
Answer: GCF of Numerators as per given numbers 306/370, 120/377 is
GCF of Numerators i.e. for 306,120 is 6
LCM of denominators i.e. for 370,377 is 139490.
Thus, GCF of Fractions is 6/139490.Finally, GCF of Fractions for 306/370, 120/377 is 6/139490.