GCF of 9774/119, 7128/455
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9774/119, 7128/455 i.e 54/7735 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9774/119, 7128/455.
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 9774/119,7128/455?
Given fractions are 9774/119,7128/455
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 9774/119,7128/455, numerators are 9774,7128
Denominators are 119,455
The GCF of 9774,7128 is 54 .
LCM of 119,455 is 7735.
The greatest common factor of 9774/119,7128/455 = [GCF of 9774,7128]/[LCM of 119,455]= 54/7735
Therefore, the GCF of 9774/119,7128/455 is 54/7735.
To find the highest common factor of 9774,7128, we have to find the factors of both numbers and list the highest common factor.
The factors of 9774 are 1, 2, 3, 6, 9, 18, 27, 54, 181, 362, 543, 1086, 1629, 3258, 4887, 9774
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 9774,7128 is 54.
Lets's calculate GCF of 9774,7128
| 2 | 9774, 7128 |
| 3 | 4887, 3564 |
| 3 | 1629, 1188 |
| 3 | 543, 396 |
| 181, 132 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 = 54
Greatest Common Factor of 9774,7128 By Matching Biggest Common Factor Method
Now, list down the factors of 9774
:1,2,3,6,9,18,27,54,181,362,543,1086,1629,3258,4887,9774
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 9774,7128 . The biggest common factor number is the GCF number.
So the greatest common factor 9774,7128 is 54.
Lets's calculate LCM of 119,455
| 7 | 119, 455 |
| 17, 65 |
∴ So the LCM of the given numbers is 7 x 17 x 65 = 7735
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 54/7735
Therefore, the GCF of Fractions 9774/119,7128/455 is 54/7735
Least Common Multiple of 119,455 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 119,455 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(119,455) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(119,455) x common factors =7 x 1 = 7
LCM(119,455) = ( 119 × 455 ) / 7
LCM(119,455) = 54145 / 7
LCM(119,455) = 7735
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FAQs on GCF of Fractions of 9774/119, 7128/455
1. What is the HCF of 9774,7128?
The HCF of 9774,7128 is 54
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 9774/119, 7128/455?
Answer: GCF of Numerators as per given numbers 9774/119, 7128/455 is
GCF of Numerators i.e. for 9774,7128 is 54
LCM of denominators i.e. for 119,455 is 7735.
Thus, GCF of Fractions is 54/7735.Finally, GCF of Fractions for 9774/119, 7128/455 is 54/7735.