Use our free GCF of Fractions Calculator tool to compute the GCF of 30/353, 312/838, 543/851 i.e 3/251737714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/353, 312/838, 543/851.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/353,312/838,543/851
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 30/353,312/838,543/851, numerators are 30,312,543
Denominators are 353,838,851
The GCF of 30,312,543 is 3 .
LCM of 353,838,851 is 251737714.
The greatest common factor of 30/353,312/838,543/851 = [GCF of 30,312,543]/[LCM of 353,838,851]= 3/251737714
Therefore, the GCF of 30/353,312/838,543/851 is 3/251737714.
To find the highest common factor of 30,312,543, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 543 are 1, 3, 181, 543
The HCF of 30,312,543 is 3.
Lets's calculate GCF of 30,312,543
3 | 30, 312, 543 |
10, 104, 181 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 543
:1,3,181,543
Greatest Common Factor
We found the factors 30,312,543 . The biggest common factor number is the GCF number.
So the greatest common factor 30,312,543 is 3.
Lets's calculate LCM of 353,838,851
Given numbers has no common factors except 1. So, there LCM is their product i.e 251737714
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/251737714
Therefore, the GCF of Fractions 30/353,312/838,543/851 is 3/251737714
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 353,838,851 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(353,838,851) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(353,838,851) x common factors =1 x 1 = 1
LCM(353,838,851) = ( 353 × 838 × 851 ) / 1
LCM(353,838,851) = 251737714 / 1
LCM(353,838,851) = 251737714
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,312,543?
The HCF of 30,312,543 is 3
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 30/353, 312/838, 543/851?
Answer: GCF of Numerators as per given numbers 30/353, 312/838, 543/851 is
GCF of Numerators i.e. for 30,312,543 is 3
LCM of denominators i.e. for 353,838,851 is 251737714.
Thus, GCF of Fractions is 3/251737714.Finally, GCF of Fractions for 30/353, 312/838, 543/851 is 3/251737714.