GCF of 98/27, 27/72, 87/86, 31/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 98/27, 27/72, 87/86, 31/16 i.e 1/18576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 98/27, 27/72, 87/86, 31/16.
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 98/27,27/72,87/86,31/16?
Given fractions are 98/27,27/72,87/86,31/16
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 98/27,27/72,87/86,31/16, numerators are 98,27,87,31
Denominators are 27,72,86,16
The GCF of 98,27,87,31 is 1 .
LCM of 27,72,86,16 is 18576.
The greatest common factor of 98/27,27/72,87/86,31/16 = [GCF of 98,27,87,31]/[LCM of 27,72,86,16]= 1/18576
Therefore, the GCF of 98/27,27/72,87/86,31/16 is 1/18576.
To find the highest common factor of 98,27,87,31, we have to find the factors of both numbers and list the highest common factor.
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 27 are 1, 3, 9, 27
The factors of 87 are 1, 3, 29, 87
The factors of 31 are 1, 31
The HCF of 98,27,87,31 is 1.
Lets's calculate GCF of 98,27,87,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 98,27,87,31 By Matching Biggest Common Factor Method
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 31
:1,31
Greatest Common Factor
We found the factors 98,27,87,31 . The biggest common factor number is the GCF number.
So the greatest common factor 98,27,87,31 is 1.
Lets's calculate LCM of 27,72,86,16
| 2 | 27, 72, 86, 16 |
| 2 | 27, 36, 43, 8 |
| 2 | 27, 18, 43, 4 |
| 3 | 27, 9, 43, 2 |
| 3 | 3, 9, 43, 2 |
| 1, 3, 43, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 1 x 3 x 43 x 2 = 18576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18576
Therefore, the GCF of Fractions 98/27,27/72,87/86,31/16 is 1/18576
Least Common Multiple of 27,72,86,16 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 27,72,86,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,72,86,16) = 1
common factors(in case of two or more numbers have common factors) = 144
GCF(27,72,86,16) x common factors =1 x 144 = 144
LCM(27,72,86,16) = ( 27 × 72 × 86 × 16 ) / 144
LCM(27,72,86,16) = 2674944 / 144
LCM(27,72,86,16) = 18576
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FAQs on GCF of Fractions of 98/27, 27/72, 87/86, 31/16
1. What is the HCF of 98,27,87,31?
The HCF of 98,27,87,31 is 1
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 98/27, 27/72, 87/86, 31/16?
Answer: GCF of Numerators as per given numbers 98/27, 27/72, 87/86, 31/16 is
GCF of Numerators i.e. for 98,27,87,31 is 1
LCM of denominators i.e. for 27,72,86,16 is 18576.
Thus, GCF of Fractions is 1/18576.Finally, GCF of Fractions for 98/27, 27/72, 87/86, 31/16 is 1/18576.