Use our free GCF of Fractions Calculator tool to compute the GCF of 54/558, 51/551, 414/597 i.e 3/61184142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/558, 51/551, 414/597.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/558,51/551,414/597
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 54/558,51/551,414/597, numerators are 54,51,414
Denominators are 558,551,597
The GCF of 54,51,414 is 3 .
LCM of 558,551,597 is 61184142.
The greatest common factor of 54/558,51/551,414/597 = [GCF of 54,51,414]/[LCM of 558,551,597]= 3/61184142
Therefore, the GCF of 54/558,51/551,414/597 is 3/61184142.
To find the highest common factor of 54,51,414, 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 51 are 1, 3, 17, 51
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 54,51,414 is 3.
Lets's calculate GCF of 54,51,414
3 | 54, 51, 414 |
18, 17, 138 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 54,51,414 . The biggest common factor number is the GCF number.
So the greatest common factor 54,51,414 is 3.
Lets's calculate LCM of 558,551,597
3 | 558, 551, 597 |
186, 551, 199 |
∴ So the LCM of the given numbers is 3 x 186 x 551 x 199 = 61184142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/61184142
Therefore, the GCF of Fractions 54/558,51/551,414/597 is 3/61184142
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 558,551,597 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(558,551,597) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(558,551,597) x common factors =1 x 3 = 3
LCM(558,551,597) = ( 558 × 551 × 597 ) / 3
LCM(558,551,597) = 183552426 / 3
LCM(558,551,597) = 61184142
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 54,51,414?
The HCF of 54,51,414 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 54/558, 51/551, 414/597?
Answer: GCF of Numerators as per given numbers 54/558, 51/551, 414/597 is
GCF of Numerators i.e. for 54,51,414 is 3
LCM of denominators i.e. for 558,551,597 is 61184142.
Thus, GCF of Fractions is 3/61184142.Finally, GCF of Fractions for 54/558, 51/551, 414/597 is 3/61184142.