GCF of 8384/542, 8509/118
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8384/542, 8509/118 i.e 1/31978 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8384/542, 8509/118.
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 8384/542,8509/118?
Given fractions are 8384/542,8509/118
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 8384/542,8509/118, numerators are 8384,8509
Denominators are 542,118
The GCF of 8384,8509 is 1 .
LCM of 542,118 is 31978.
The greatest common factor of 8384/542,8509/118 = [GCF of 8384,8509]/[LCM of 542,118]= 1/31978
Therefore, the GCF of 8384/542,8509/118 is 1/31978.
To find the highest common factor of 8384,8509, we have to find the factors of both numbers and list the highest common factor.
The factors of 8384 are 1, 2, 4, 8, 16, 32, 64, 131, 262, 524, 1048, 2096, 4192, 8384
The factors of 8509 are 1, 67, 127, 8509
The HCF of 8384,8509 is 1.
Lets's calculate GCF of 8384,8509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8384,8509 By Matching Biggest Common Factor Method
Now, list down the factors of 8384
:1,2,4,8,16,32,64,131,262,524,1048,2096,4192,8384
Now, list down the factors of 8509
:1,67,127,8509
Greatest Common Factor
We found the factors 8384,8509 . The biggest common factor number is the GCF number.
So the greatest common factor 8384,8509 is 1.
Lets's calculate LCM of 542,118
| 2 | 542, 118 |
| 271, 59 |
∴ So the LCM of the given numbers is 2 x 271 x 59 = 31978
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31978
Therefore, the GCF of Fractions 8384/542,8509/118 is 1/31978
Least Common Multiple of 542,118 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 542,118 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(542,118) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(542,118) x common factors =2 x 1 = 2
LCM(542,118) = ( 542 × 118 ) / 2
LCM(542,118) = 63956 / 2
LCM(542,118) = 31978
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FAQs on GCF of Fractions of 8384/542, 8509/118
1. What is the HCF of 8384,8509?
The HCF of 8384,8509 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 8384/542, 8509/118?
Answer: GCF of Numerators as per given numbers 8384/542, 8509/118 is
GCF of Numerators i.e. for 8384,8509 is 1
LCM of denominators i.e. for 542,118 is 31978.
Thus, GCF of Fractions is 1/31978.Finally, GCF of Fractions for 8384/542, 8509/118 is 1/31978.