GCF of 4122/422, 6138/5108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4122/422, 6138/5108 i.e 18/1077788 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4122/422, 6138/5108.
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 4122/422,6138/5108?
Given fractions are 4122/422,6138/5108
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 4122/422,6138/5108, numerators are 4122,6138
Denominators are 422,5108
The GCF of 4122,6138 is 18 .
LCM of 422,5108 is 1077788.
The greatest common factor of 4122/422,6138/5108 = [GCF of 4122,6138]/[LCM of 422,5108]= 18/1077788
Therefore, the GCF of 4122/422,6138/5108 is 18/1077788.
To find the highest common factor of 4122,6138, we have to find the factors of both numbers and list the highest common factor.
The factors of 4122 are 1, 2, 3, 6, 9, 18, 229, 458, 687, 1374, 2061, 4122
The factors of 6138 are 1, 2, 3, 6, 9, 11, 18, 22, 31, 33, 62, 66, 93, 99, 186, 198, 279, 341, 558, 682, 1023, 2046, 3069, 6138
The HCF of 4122,6138 is 18.
Lets's calculate GCF of 4122,6138
| 2 | 4122, 6138 |
| 3 | 2061, 3069 |
| 3 | 687, 1023 |
| 229, 341 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 4122,6138 By Matching Biggest Common Factor Method
Now, list down the factors of 4122
:1,2,3,6,9,18,229,458,687,1374,2061,4122
Now, list down the factors of 6138
:1,2,3,6,9,11,18,22,31,33,62,66,93,99,186,198,279,341,558,682,1023,2046,3069,6138
Greatest Common Factor
We found the factors 4122,6138 . The biggest common factor number is the GCF number.
So the greatest common factor 4122,6138 is 18.
Lets's calculate LCM of 422,5108
| 2 | 422, 5108 |
| 211, 2554 |
∴ So the LCM of the given numbers is 2 x 211 x 2554 = 1077788
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/1077788
Therefore, the GCF of Fractions 4122/422,6138/5108 is 18/1077788
Least Common Multiple of 422,5108 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 422,5108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(422,5108) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(422,5108) x common factors =2 x 1 = 2
LCM(422,5108) = ( 422 × 5108 ) / 2
LCM(422,5108) = 2155576 / 2
LCM(422,5108) = 1077788
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FAQs on GCF of Fractions of 4122/422, 6138/5108
1. What is the HCF of 4122,6138?
The HCF of 4122,6138 is 18
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 4122/422, 6138/5108?
Answer: GCF of Numerators as per given numbers 4122/422, 6138/5108 is
GCF of Numerators i.e. for 4122,6138 is 18
LCM of denominators i.e. for 422,5108 is 1077788.
Thus, GCF of Fractions is 18/1077788.Finally, GCF of Fractions for 4122/422, 6138/5108 is 18/1077788.