Use our free GCF of Fractions Calculator tool to compute the GCF of 78/35, 214/33, 783/300 i.e 1/23100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/35, 214/33, 783/300.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/35,214/33,783/300
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 78/35,214/33,783/300, numerators are 78,214,783
Denominators are 35,33,300
The GCF of 78,214,783 is 1 .
LCM of 35,33,300 is 23100.
The greatest common factor of 78/35,214/33,783/300 = [GCF of 78,214,783]/[LCM of 35,33,300]= 1/23100
Therefore, the GCF of 78/35,214/33,783/300 is 1/23100.
To find the highest common factor of 78,214,783, 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 214 are 1, 2, 107, 214
The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783
The HCF of 78,214,783 is 1.
Lets's calculate GCF of 78,214,783
∴ 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 214
:1,2,107,214
Now, list down the factors of 783
:1,3,9,27,29,87,261,783
Greatest Common Factor
We found the factors 78,214,783 . The biggest common factor number is the GCF number.
So the greatest common factor 78,214,783 is 1.
Lets's calculate LCM of 35,33,300
3 | 35, 33, 300 |
5 | 35, 11, 100 |
7, 11, 20 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 11 x 20 = 23100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23100
Therefore, the GCF of Fractions 78/35,214/33,783/300 is 1/23100
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 35,33,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,33,300) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(35,33,300) x common factors =1 x 15 = 15
LCM(35,33,300) = ( 35 × 33 × 300 ) / 15
LCM(35,33,300) = 346500 / 15
LCM(35,33,300) = 23100
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 78,214,783?
The HCF of 78,214,783 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 78/35, 214/33, 783/300?
Answer: GCF of Numerators as per given numbers 78/35, 214/33, 783/300 is
GCF of Numerators i.e. for 78,214,783 is 1
LCM of denominators i.e. for 35,33,300 is 23100.
Thus, GCF of Fractions is 1/23100.Finally, GCF of Fractions for 78/35, 214/33, 783/300 is 1/23100.