GCF of 7161/871, 8184/5941
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7161/871, 8184/5941 i.e 1023/398047 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7161/871, 8184/5941.
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 7161/871,8184/5941?
Given fractions are 7161/871,8184/5941
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 7161/871,8184/5941, numerators are 7161,8184
Denominators are 871,5941
The GCF of 7161,8184 is 1023 .
LCM of 871,5941 is 398047.
The greatest common factor of 7161/871,8184/5941 = [GCF of 7161,8184]/[LCM of 871,5941]= 1023/398047
Therefore, the GCF of 7161/871,8184/5941 is 1023/398047.
To find the highest common factor of 7161,8184, we have to find the factors of both numbers and list the highest common factor.
The factors of 7161 are 1, 3, 7, 11, 21, 31, 33, 77, 93, 217, 231, 341, 651, 1023, 2387, 7161
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 7161,8184 is 1023.
Lets's calculate GCF of 7161,8184
| 3 | 7161, 8184 |
| 11 | 2387, 2728 |
| 31 | 217, 248 |
| 7, 8 |
∴ So the GCF of the given numbers is 3 x 11 x 31 = 1023
Greatest Common Factor of 7161,8184 By Matching Biggest Common Factor Method
Now, list down the factors of 7161
:1,3,7,11,21,31,33,77,93,217,231,341,651,1023,2387,7161
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 7161,8184 . The biggest common factor number is the GCF number.
So the greatest common factor 7161,8184 is 1023.
Lets's calculate LCM of 871,5941
| 13 | 871, 5941 |
| 67, 457 |
∴ So the LCM of the given numbers is 13 x 67 x 457 = 398047
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1023/398047
Therefore, the GCF of Fractions 7161/871,8184/5941 is 1023/398047
Least Common Multiple of 871,5941 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 871,5941 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(871,5941) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(871,5941) x common factors =13 x 1 = 13
LCM(871,5941) = ( 871 × 5941 ) / 13
LCM(871,5941) = 5174611 / 13
LCM(871,5941) = 398047
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FAQs on GCF of Fractions of 7161/871, 8184/5941
1. What is the HCF of 7161,8184?
The HCF of 7161,8184 is 1023
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 7161/871, 8184/5941?
Answer: GCF of Numerators as per given numbers 7161/871, 8184/5941 is
GCF of Numerators i.e. for 7161,8184 is 1023
LCM of denominators i.e. for 871,5941 is 398047.
Thus, GCF of Fractions is 1023/398047.Finally, GCF of Fractions for 7161/871, 8184/5941 is 1023/398047.