GCF of 1131/908, 8184/5824
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1131/908, 8184/5824 i.e 3/1322048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1131/908, 8184/5824.
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 1131/908,8184/5824?
Given fractions are 1131/908,8184/5824
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 1131/908,8184/5824, numerators are 1131,8184
Denominators are 908,5824
The GCF of 1131,8184 is 3 .
LCM of 908,5824 is 1322048.
The greatest common factor of 1131/908,8184/5824 = [GCF of 1131,8184]/[LCM of 908,5824]= 3/1322048
Therefore, the GCF of 1131/908,8184/5824 is 3/1322048.
To find the highest common factor of 1131,8184, we have to find the factors of both numbers and list the highest common factor.
The factors of 1131 are 1, 3, 13, 29, 39, 87, 377, 1131
The factors of 8184 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 31, 33, 44, 62, 66, 88, 93, 124, 132, 186, 248, 264, 341, 372, 682, 744, 1023, 1364, 2046, 2728, 4092, 8184
The HCF of 1131,8184 is 3.
Lets's calculate GCF of 1131,8184
| 3 | 1131, 8184 |
| 377, 2728 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1131,8184 By Matching Biggest Common Factor Method
Now, list down the factors of 1131
:1,3,13,29,39,87,377,1131
Now, list down the factors of 8184
:1,2,3,4,6,8,11,12,22,24,31,33,44,62,66,88,93,124,132,186,248,264,341,372,682,744,1023,1364,2046,2728,4092,8184
Greatest Common Factor
We found the factors 1131,8184 . The biggest common factor number is the GCF number.
So the greatest common factor 1131,8184 is 3.
Lets's calculate LCM of 908,5824
| 2 | 908, 5824 |
| 2 | 454, 2912 |
| 227, 1456 |
∴ So the LCM of the given numbers is 2 x 2 x 227 x 1456 = 1322048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1322048
Therefore, the GCF of Fractions 1131/908,8184/5824 is 3/1322048
Least Common Multiple of 908,5824 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 908,5824 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(908,5824) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(908,5824) x common factors =4 x 1 = 4
LCM(908,5824) = ( 908 × 5824 ) / 4
LCM(908,5824) = 5288192 / 4
LCM(908,5824) = 1322048
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FAQs on GCF of Fractions of 1131/908, 8184/5824
1. What is the HCF of 1131,8184?
The HCF of 1131,8184 is 3
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 1131/908, 8184/5824?
Answer: GCF of Numerators as per given numbers 1131/908, 8184/5824 is
GCF of Numerators i.e. for 1131,8184 is 3
LCM of denominators i.e. for 908,5824 is 1322048.
Thus, GCF of Fractions is 3/1322048.Finally, GCF of Fractions for 1131/908, 8184/5824 is 3/1322048.