GCF of 7128/238, 4185/203
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7128/238, 4185/203 i.e 27/6902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7128/238, 4185/203.
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 7128/238,4185/203?
Given fractions are 7128/238,4185/203
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 7128/238,4185/203, numerators are 7128,4185
Denominators are 238,203
The GCF of 7128,4185 is 27 .
LCM of 238,203 is 6902.
The greatest common factor of 7128/238,4185/203 = [GCF of 7128,4185]/[LCM of 238,203]= 27/6902
Therefore, the GCF of 7128/238,4185/203 is 27/6902.
To find the highest common factor of 7128,4185, we have to find the factors of both numbers and list the highest common factor.
The factors of 7128 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 44, 54, 66, 72, 81, 88, 99, 108, 132, 162, 198, 216, 264, 297, 324, 396, 594, 648, 792, 891, 1188, 1782, 2376, 3564, 7128
The factors of 4185 are 1, 3, 5, 9, 15, 27, 31, 45, 93, 135, 155, 279, 465, 837, 1395, 4185
The HCF of 7128,4185 is 27.
Lets's calculate GCF of 7128,4185
| 3 | 7128, 4185 |
| 3 | 2376, 1395 |
| 3 | 792, 465 |
| 264, 155 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 7128,4185 By Matching Biggest Common Factor Method
Now, list down the factors of 7128
:1,2,3,4,6,8,9,11,12,18,22,24,27,33,36,44,54,66,72,81,88,99,108,132,162,198,216,264,297,324,396,594,648,792,891,1188,1782,2376,3564,7128
Now, list down the factors of 4185
:1,3,5,9,15,27,31,45,93,135,155,279,465,837,1395,4185
Greatest Common Factor
We found the factors 7128,4185 . The biggest common factor number is the GCF number.
So the greatest common factor 7128,4185 is 27.
Lets's calculate LCM of 238,203
| 7 | 238, 203 |
| 34, 29 |
∴ So the LCM of the given numbers is 7 x 34 x 29 = 6902
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/6902
Therefore, the GCF of Fractions 7128/238,4185/203 is 27/6902
Least Common Multiple of 238,203 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 238,203 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(238,203) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(238,203) x common factors =7 x 1 = 7
LCM(238,203) = ( 238 × 203 ) / 7
LCM(238,203) = 48314 / 7
LCM(238,203) = 6902
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FAQs on GCF of Fractions of 7128/238, 4185/203
1. What is the HCF of 7128,4185?
The HCF of 7128,4185 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 7128/238, 4185/203?
Answer: GCF of Numerators as per given numbers 7128/238, 4185/203 is
GCF of Numerators i.e. for 7128,4185 is 27
LCM of denominators i.e. for 238,203 is 6902.
Thus, GCF of Fractions is 27/6902.Finally, GCF of Fractions for 7128/238, 4185/203 is 27/6902.