GCF of 6006/329, 7128/141
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6006/329, 7128/141 i.e 66/987 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6006/329, 7128/141.
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 6006/329,7128/141?
Given fractions are 6006/329,7128/141
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 6006/329,7128/141, numerators are 6006,7128
Denominators are 329,141
The GCF of 6006,7128 is 66 .
LCM of 329,141 is 987.
The greatest common factor of 6006/329,7128/141 = [GCF of 6006,7128]/[LCM of 329,141]= 66/987
Therefore, the GCF of 6006/329,7128/141 is 66/987.
To find the highest common factor of 6006,7128, we have to find the factors of both numbers and list the highest common factor.
The factors of 6006 are 1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 143, 154, 182, 231, 273, 286, 429, 462, 546, 858, 1001, 2002, 3003, 6006
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 HCF of 6006,7128 is 66.
Lets's calculate GCF of 6006,7128
| 2 | 6006, 7128 |
| 3 | 3003, 3564 |
| 11 | 1001, 1188 |
| 91, 108 |
∴ So the GCF of the given numbers is 2 x 3 x 11 = 66
Greatest Common Factor of 6006,7128 By Matching Biggest Common Factor Method
Now, list down the factors of 6006
:1,2,3,6,7,11,13,14,21,22,26,33,39,42,66,77,78,91,143,154,182,231,273,286,429,462,546,858,1001,2002,3003,6006
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
Greatest Common Factor
We found the factors 6006,7128 . The biggest common factor number is the GCF number.
So the greatest common factor 6006,7128 is 66.
Lets's calculate LCM of 329,141
| 47 | 329, 141 |
| 7, 3 |
∴ So the LCM of the given numbers is 47 x 7 x 3 = 987
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 66/987
Therefore, the GCF of Fractions 6006/329,7128/141 is 66/987
Least Common Multiple of 329,141 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 329,141 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(329,141) = 47
common factors(in case of two or more numbers have common factors) = 1
GCF(329,141) x common factors =47 x 1 = 47
LCM(329,141) = ( 329 × 141 ) / 47
LCM(329,141) = 46389 / 47
LCM(329,141) = 987
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FAQs on GCF of Fractions of 6006/329, 7128/141
1. What is the HCF of 6006,7128?
The HCF of 6006,7128 is 66
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 6006/329, 7128/141?
Answer: GCF of Numerators as per given numbers 6006/329, 7128/141 is
GCF of Numerators i.e. for 6006,7128 is 66
LCM of denominators i.e. for 329,141 is 987.
Thus, GCF of Fractions is 66/987.Finally, GCF of Fractions for 6006/329, 7128/141 is 66/987.