Use our free GCF of Fractions Calculator tool to compute the GCF of 764/642, 120/105 i.e 4/22470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 764/642, 120/105.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 764/642,120/105
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 764/642,120/105, numerators are 764,120
Denominators are 642,105
The GCF of 764,120 is 4 .
LCM of 642,105 is 22470.
The greatest common factor of 764/642,120/105 = [GCF of 764,120]/[LCM of 642,105]= 4/22470
Therefore, the GCF of 764/642,120/105 is 4/22470.
To find the highest common factor of 764,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 764 are 1, 2, 4, 191, 382, 764
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 764,120 is 4.
Lets's calculate GCF of 764,120
2 | 764, 120 |
2 | 382, 60 |
191, 30 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 764
:1,2,4,191,382,764
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 764,120 . The biggest common factor number is the GCF number.
So the greatest common factor 764,120 is 4.
Lets's calculate LCM of 642,105
3 | 642, 105 |
214, 35 |
∴ So the LCM of the given numbers is 3 x 214 x 35 = 22470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/22470
Therefore, the GCF of Fractions 764/642,120/105 is 4/22470
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 642,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(642,105) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(642,105) x common factors =3 x 1 = 3
LCM(642,105) = ( 642 × 105 ) / 3
LCM(642,105) = 67410 / 3
LCM(642,105) = 22470
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 764,120?
The HCF of 764,120 is 4
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 764/642, 120/105?
Answer: GCF of Numerators as per given numbers 764/642, 120/105 is
GCF of Numerators i.e. for 764,120 is 4
LCM of denominators i.e. for 642,105 is 22470.
Thus, GCF of Fractions is 4/22470.Finally, GCF of Fractions for 764/642, 120/105 is 4/22470.