Use our free GCF of Fractions Calculator tool to compute the GCF of 30/559, 35/575, 400/851 i.e 5/11892725 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/559, 35/575, 400/851.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/559,35/575,400/851
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 30/559,35/575,400/851, numerators are 30,35,400
Denominators are 559,575,851
The GCF of 30,35,400 is 5 .
LCM of 559,575,851 is 11892725.
The greatest common factor of 30/559,35/575,400/851 = [GCF of 30,35,400]/[LCM of 559,575,851]= 5/11892725
Therefore, the GCF of 30/559,35/575,400/851 is 5/11892725.
To find the highest common factor of 30,35,400, 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 35 are 1, 5, 7, 35
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 30,35,400 is 5.
Lets's calculate GCF of 30,35,400
5 | 30, 35, 400 |
6, 7, 80 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 30,35,400 . The biggest common factor number is the GCF number.
So the greatest common factor 30,35,400 is 5.
Lets's calculate LCM of 559,575,851
23 | 559, 575, 851 |
559, 25, 37 |
∴ So the LCM of the given numbers is 23 x 559 x 25 x 37 = 11892725
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/11892725
Therefore, the GCF of Fractions 30/559,35/575,400/851 is 5/11892725
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 559,575,851 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(559,575,851) = 1
common factors(in case of two or more numbers have common factors) = 23
GCF(559,575,851) x common factors =1 x 23 = 23
LCM(559,575,851) = ( 559 × 575 × 851 ) / 23
LCM(559,575,851) = 273532675 / 23
LCM(559,575,851) = 11892725
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,35,400?
The HCF of 30,35,400 is 5
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 30/559, 35/575, 400/851?
Answer: GCF of Numerators as per given numbers 30/559, 35/575, 400/851 is
GCF of Numerators i.e. for 30,35,400 is 5
LCM of denominators i.e. for 559,575,851 is 11892725.
Thus, GCF of Fractions is 5/11892725.Finally, GCF of Fractions for 30/559, 35/575, 400/851 is 5/11892725.