GCF of 8127/132, 9738/1842
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8127/132, 9738/1842 i.e 9/40524 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8127/132, 9738/1842.
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 8127/132,9738/1842?
Given fractions are 8127/132,9738/1842
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 8127/132,9738/1842, numerators are 8127,9738
Denominators are 132,1842
The GCF of 8127,9738 is 9 .
LCM of 132,1842 is 40524.
The greatest common factor of 8127/132,9738/1842 = [GCF of 8127,9738]/[LCM of 132,1842]= 9/40524
Therefore, the GCF of 8127/132,9738/1842 is 9/40524.
To find the highest common factor of 8127,9738, we have to find the factors of both numbers and list the highest common factor.
The factors of 8127 are 1, 3, 7, 9, 21, 27, 43, 63, 129, 189, 301, 387, 903, 1161, 2709, 8127
The factors of 9738 are 1, 2, 3, 6, 9, 18, 541, 1082, 1623, 3246, 4869, 9738
The HCF of 8127,9738 is 9.
Lets's calculate GCF of 8127,9738
| 3 | 8127, 9738 |
| 3 | 2709, 3246 |
| 903, 1082 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 8127,9738 By Matching Biggest Common Factor Method
Now, list down the factors of 8127
:1,3,7,9,21,27,43,63,129,189,301,387,903,1161,2709,8127
Now, list down the factors of 9738
:1,2,3,6,9,18,541,1082,1623,3246,4869,9738
Greatest Common Factor
We found the factors 8127,9738 . The biggest common factor number is the GCF number.
So the greatest common factor 8127,9738 is 9.
Lets's calculate LCM of 132,1842
| 2 | 132, 1842 |
| 3 | 66, 921 |
| 22, 307 |
∴ So the LCM of the given numbers is 2 x 3 x 22 x 307 = 40524
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/40524
Therefore, the GCF of Fractions 8127/132,9738/1842 is 9/40524
Least Common Multiple of 132,1842 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 132,1842 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,1842) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(132,1842) x common factors =6 x 1 = 6
LCM(132,1842) = ( 132 × 1842 ) / 6
LCM(132,1842) = 243144 / 6
LCM(132,1842) = 40524
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FAQs on GCF of Fractions of 8127/132, 9738/1842
1. What is the HCF of 8127,9738?
The HCF of 8127,9738 is 9
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 8127/132, 9738/1842?
Answer: GCF of Numerators as per given numbers 8127/132, 9738/1842 is
GCF of Numerators i.e. for 8127,9738 is 9
LCM of denominators i.e. for 132,1842 is 40524.
Thus, GCF of Fractions is 9/40524.Finally, GCF of Fractions for 8127/132, 9738/1842 is 9/40524.