GCF of 4182/172, 5746/284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4182/172, 5746/284 i.e 34/12212 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4182/172, 5746/284.
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 4182/172,5746/284?
Given fractions are 4182/172,5746/284
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 4182/172,5746/284, numerators are 4182,5746
Denominators are 172,284
The GCF of 4182,5746 is 34 .
LCM of 172,284 is 12212.
The greatest common factor of 4182/172,5746/284 = [GCF of 4182,5746]/[LCM of 172,284]= 34/12212
Therefore, the GCF of 4182/172,5746/284 is 34/12212.
To find the highest common factor of 4182,5746, we have to find the factors of both numbers and list the highest common factor.
The factors of 4182 are 1, 2, 3, 6, 17, 34, 41, 51, 82, 102, 123, 246, 697, 1394, 2091, 4182
The factors of 5746 are 1, 2, 13, 17, 26, 34, 169, 221, 338, 442, 2873, 5746
The HCF of 4182,5746 is 34.
Lets's calculate GCF of 4182,5746
| 2 | 4182, 5746 |
| 17 | 2091, 2873 |
| 123, 169 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 4182,5746 By Matching Biggest Common Factor Method
Now, list down the factors of 4182
:1,2,3,6,17,34,41,51,82,102,123,246,697,1394,2091,4182
Now, list down the factors of 5746
:1,2,13,17,26,34,169,221,338,442,2873,5746
Greatest Common Factor
We found the factors 4182,5746 . The biggest common factor number is the GCF number.
So the greatest common factor 4182,5746 is 34.
Lets's calculate LCM of 172,284
| 2 | 172, 284 |
| 2 | 86, 142 |
| 43, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 71 = 12212
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/12212
Therefore, the GCF of Fractions 4182/172,5746/284 is 34/12212
Least Common Multiple of 172,284 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 172,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,284) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(172,284) x common factors =4 x 1 = 4
LCM(172,284) = ( 172 × 284 ) / 4
LCM(172,284) = 48848 / 4
LCM(172,284) = 12212
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FAQs on GCF of Fractions of 4182/172, 5746/284
1. What is the HCF of 4182,5746?
The HCF of 4182,5746 is 34
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 4182/172, 5746/284?
Answer: GCF of Numerators as per given numbers 4182/172, 5746/284 is
GCF of Numerators i.e. for 4182,5746 is 34
LCM of denominators i.e. for 172,284 is 12212.
Thus, GCF of Fractions is 34/12212.Finally, GCF of Fractions for 4182/172, 5746/284 is 34/12212.