GCF of 7419/414, 1092/276
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7419/414, 1092/276 i.e 3/828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7419/414, 1092/276.
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 7419/414,1092/276?
Given fractions are 7419/414,1092/276
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 7419/414,1092/276, numerators are 7419,1092
Denominators are 414,276
The GCF of 7419,1092 is 3 .
LCM of 414,276 is 828.
The greatest common factor of 7419/414,1092/276 = [GCF of 7419,1092]/[LCM of 414,276]= 3/828
Therefore, the GCF of 7419/414,1092/276 is 3/828.
To find the highest common factor of 7419,1092, we have to find the factors of both numbers and list the highest common factor.
The factors of 7419 are 1, 3, 2473, 7419
The factors of 1092 are 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092
The HCF of 7419,1092 is 3.
Lets's calculate GCF of 7419,1092
| 3 | 7419, 1092 |
| 2473, 364 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7419,1092 By Matching Biggest Common Factor Method
Now, list down the factors of 7419
:1,3,2473,7419
Now, list down the factors of 1092
:1,2,3,4,6,7,12,13,14,21,26,28,39,42,52,78,84,91,156,182,273,364,546,1092
Greatest Common Factor
We found the factors 7419,1092 . The biggest common factor number is the GCF number.
So the greatest common factor 7419,1092 is 3.
Lets's calculate LCM of 414,276
| 2 | 414, 276 |
| 3 | 207, 138 |
| 23 | 69, 46 |
| 3, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 23 x 3 x 2 = 828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/828
Therefore, the GCF of Fractions 7419/414,1092/276 is 3/828
Least Common Multiple of 414,276 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 414,276 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,276) = 138
common factors(in case of two or more numbers have common factors) = 1
GCF(414,276) x common factors =138 x 1 = 138
LCM(414,276) = ( 414 × 276 ) / 138
LCM(414,276) = 114264 / 138
LCM(414,276) = 828
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FAQs on GCF of Fractions of 7419/414, 1092/276
1. What is the HCF of 7419,1092?
The HCF of 7419,1092 is 3
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 7419/414, 1092/276?
Answer: GCF of Numerators as per given numbers 7419/414, 1092/276 is
GCF of Numerators i.e. for 7419,1092 is 3
LCM of denominators i.e. for 414,276 is 828.
Thus, GCF of Fractions is 3/828.Finally, GCF of Fractions for 7419/414, 1092/276 is 3/828.