GCF of 9261/208, 5724/106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9261/208, 5724/106 i.e 27/11024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9261/208, 5724/106.
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 9261/208,5724/106?
Given fractions are 9261/208,5724/106
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 9261/208,5724/106, numerators are 9261,5724
Denominators are 208,106
The GCF of 9261,5724 is 27 .
LCM of 208,106 is 11024.
The greatest common factor of 9261/208,5724/106 = [GCF of 9261,5724]/[LCM of 208,106]= 27/11024
Therefore, the GCF of 9261/208,5724/106 is 27/11024.
To find the highest common factor of 9261,5724, we have to find the factors of both numbers and list the highest common factor.
The factors of 9261 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 343, 441, 1029, 1323, 3087, 9261
The factors of 5724 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 53, 54, 106, 108, 159, 212, 318, 477, 636, 954, 1431, 1908, 2862, 5724
The HCF of 9261,5724 is 27.
Lets's calculate GCF of 9261,5724
| 3 | 9261, 5724 |
| 3 | 3087, 1908 |
| 3 | 1029, 636 |
| 343, 212 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 9261,5724 By Matching Biggest Common Factor Method
Now, list down the factors of 9261
:1,3,7,9,21,27,49,63,147,189,343,441,1029,1323,3087,9261
Now, list down the factors of 5724
:1,2,3,4,6,9,12,18,27,36,53,54,106,108,159,212,318,477,636,954,1431,1908,2862,5724
Greatest Common Factor
We found the factors 9261,5724 . The biggest common factor number is the GCF number.
So the greatest common factor 9261,5724 is 27.
Lets's calculate LCM of 208,106
| 2 | 208, 106 |
| 104, 53 |
∴ So the LCM of the given numbers is 2 x 104 x 53 = 11024
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/11024
Therefore, the GCF of Fractions 9261/208,5724/106 is 27/11024
Least Common Multiple of 208,106 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 208,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,106) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(208,106) x common factors =2 x 1 = 2
LCM(208,106) = ( 208 × 106 ) / 2
LCM(208,106) = 22048 / 2
LCM(208,106) = 11024
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FAQs on GCF of Fractions of 9261/208, 5724/106
1. What is the HCF of 9261,5724?
The HCF of 9261,5724 is 27
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 9261/208, 5724/106?
Answer: GCF of Numerators as per given numbers 9261/208, 5724/106 is
GCF of Numerators i.e. for 9261,5724 is 27
LCM of denominators i.e. for 208,106 is 11024.
Thus, GCF of Fractions is 27/11024.Finally, GCF of Fractions for 9261/208, 5724/106 is 27/11024.