GCF of 558/27, 713/108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 558/27, 713/108 i.e 31/108 easily. The following is the detailed procedure to determine the greatest common factor of fractions 558/27, 713/108.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 558/27,713/108?
Given fractions are 558/27,713/108
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 558/27,713/108, numerators are 558,713
Denominators are 27,108
The GCF of 558,713 is 31 .
LCM of 27,108 is 108.
The greatest common factor of 558/27,713/108 = [GCF of 558,713]/[LCM of 27,108]= 31/108
Therefore, the GCF of 558/27,713/108 is 31/108.
To find the highest common factor of 558,713, we have to find the factors of both numbers and list the highest common factor.
The factors of 558 are 1, 2, 3, 6, 9, 18, 31, 62, 93, 186, 279, 558
The factors of 713 are 1, 23, 31, 713
The HCF of 558,713 is 31.
Lets's calculate GCF of 558,713
| 31 | 558, 713 |
| 18, 23 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 558,713 By Matching Biggest Common Factor Method
Now, list down the factors of 558
:1,2,3,6,9,18,31,62,93,186,279,558
Now, list down the factors of 713
:1,23,31,713
Greatest Common Factor
We found the factors 558,713 . The biggest common factor number is the GCF number.
So the greatest common factor 558,713 is 31.
Lets's calculate LCM of 27,108
| 3 | 27, 108 |
| 3 | 9, 36 |
| 3 | 3, 12 |
| 1, 4 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 1 x 4 = 108
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/108
Therefore, the GCF of Fractions 558/27,713/108 is 31/108
Least Common Multiple of 27,108 with GCF Formula
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 27,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,108) = 27
common factors(in case of two or more numbers have common factors) = 1
GCF(27,108) x common factors =27 x 1 = 27
LCM(27,108) = ( 27 × 108 ) / 27
LCM(27,108) = 2916 / 27
LCM(27,108) = 108
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FAQs on GCF of Fractions of 558/27, 713/108
1. What is the HCF of 558,713?
The HCF of 558,713 is 31
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 558/27, 713/108?
Answer: GCF of Numerators as per given numbers 558/27, 713/108 is
GCF of Numerators i.e. for 558,713 is 31
LCM of denominators i.e. for 27,108 is 108.
Thus, GCF of Fractions is 31/108.Finally, GCF of Fractions for 558/27, 713/108 is 31/108.