Use our free GCF of Fractions Calculator tool to compute the GCF of 54/51, 560/55, 936/140 i.e 2/78540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/51, 560/55, 936/140.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/51,560/55,936/140
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 54/51,560/55,936/140, numerators are 54,560,936
Denominators are 51,55,140
The GCF of 54,560,936 is 2 .
LCM of 51,55,140 is 78540.
The greatest common factor of 54/51,560/55,936/140 = [GCF of 54,560,936]/[LCM of 51,55,140]= 2/78540
Therefore, the GCF of 54/51,560/55,936/140 is 2/78540.
To find the highest common factor of 54,560,936, we have to find the factors of both numbers and list the highest common factor.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The factors of 936 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936
The HCF of 54,560,936 is 2.
Lets's calculate GCF of 54,560,936
2 | 54, 560, 936 |
27, 280, 468 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Now, list down the factors of 936
:1,2,3,4,6,8,9,12,13,18,24,26,36,39,52,72,78,104,117,156,234,312,468,936
Greatest Common Factor
We found the factors 54,560,936 . The biggest common factor number is the GCF number.
So the greatest common factor 54,560,936 is 2.
Lets's calculate LCM of 51,55,140
5 | 51, 55, 140 |
51, 11, 28 |
∴ So the LCM of the given numbers is 5 x 51 x 11 x 28 = 78540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/78540
Therefore, the GCF of Fractions 54/51,560/55,936/140 is 2/78540
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 51,55,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,55,140) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(51,55,140) x common factors =1 x 5 = 5
LCM(51,55,140) = ( 51 × 55 × 140 ) / 5
LCM(51,55,140) = 392700 / 5
LCM(51,55,140) = 78540
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 54,560,936?
The HCF of 54,560,936 is 2
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 54/51, 560/55, 936/140?
Answer: GCF of Numerators as per given numbers 54/51, 560/55, 936/140 is
GCF of Numerators i.e. for 54,560,936 is 2
LCM of denominators i.e. for 51,55,140 is 78540.
Thus, GCF of Fractions is 2/78540.Finally, GCF of Fractions for 54/51, 560/55, 936/140 is 2/78540.