Use our free GCF of Fractions Calculator tool to compute the GCF of 300/821, 102/708 i.e 6/581268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/821, 102/708.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 300/821,102/708
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 300/821,102/708, numerators are 300,102
Denominators are 821,708
The GCF of 300,102 is 6 .
LCM of 821,708 is 581268.
The greatest common factor of 300/821,102/708 = [GCF of 300,102]/[LCM of 821,708]= 6/581268
Therefore, the GCF of 300/821,102/708 is 6/581268.
To find the highest common factor of 300,102, we have to find the factors of both numbers and list the highest common factor.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The HCF of 300,102 is 6.
Lets's calculate GCF of 300,102
2 | 300, 102 |
3 | 150, 51 |
50, 17 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Greatest Common Factor
We found the factors 300,102 . The biggest common factor number is the GCF number.
So the greatest common factor 300,102 is 6.
Lets's calculate LCM of 821,708
Given numbers has no common factors except 1. So, there LCM is their product i.e 581268
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/581268
Therefore, the GCF of Fractions 300/821,102/708 is 6/581268
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 821,708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,708) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,708) x common factors =1 x 1 = 1
LCM(821,708) = ( 821 × 708 ) / 1
LCM(821,708) = 581268 / 1
LCM(821,708) = 581268
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 300,102?
The HCF of 300,102 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 300/821, 102/708?
Answer: GCF of Numerators as per given numbers 300/821, 102/708 is
GCF of Numerators i.e. for 300,102 is 6
LCM of denominators i.e. for 821,708 is 581268.
Thus, GCF of Fractions is 6/581268.Finally, GCF of Fractions for 300/821, 102/708 is 6/581268.