GCF of 378/414, 8631/2244
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 378/414, 8631/2244 i.e 63/154836 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/414, 8631/2244.
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 378/414,8631/2244?
Given fractions are 378/414,8631/2244
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 378/414,8631/2244, numerators are 378,8631
Denominators are 414,2244
The GCF of 378,8631 is 63 .
LCM of 414,2244 is 154836.
The greatest common factor of 378/414,8631/2244 = [GCF of 378,8631]/[LCM of 414,2244]= 63/154836
Therefore, the GCF of 378/414,8631/2244 is 63/154836.
To find the highest common factor of 378,8631, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 8631 are 1, 3, 7, 9, 21, 63, 137, 411, 959, 1233, 2877, 8631
The HCF of 378,8631 is 63.
Lets's calculate GCF of 378,8631
| 3 | 378, 8631 |
| 3 | 126, 2877 |
| 7 | 42, 959 |
| 6, 137 |
∴ So the GCF of the given numbers is 3 x 3 x 7 = 63
Greatest Common Factor of 378,8631 By Matching Biggest Common Factor Method
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 8631
:1,3,7,9,21,63,137,411,959,1233,2877,8631
Greatest Common Factor
We found the factors 378,8631 . The biggest common factor number is the GCF number.
So the greatest common factor 378,8631 is 63.
Lets's calculate LCM of 414,2244
| 2 | 414, 2244 |
| 3 | 207, 1122 |
| 69, 374 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 374 = 154836
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 63/154836
Therefore, the GCF of Fractions 378/414,8631/2244 is 63/154836
Least Common Multiple of 414,2244 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 414,2244 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,2244) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,2244) x common factors =6 x 1 = 6
LCM(414,2244) = ( 414 × 2244 ) / 6
LCM(414,2244) = 929016 / 6
LCM(414,2244) = 154836
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FAQs on GCF of Fractions of 378/414, 8631/2244
1. What is the HCF of 378,8631?
The HCF of 378,8631 is 63
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 378/414, 8631/2244?
Answer: GCF of Numerators as per given numbers 378/414, 8631/2244 is
GCF of Numerators i.e. for 378,8631 is 63
LCM of denominators i.e. for 414,2244 is 154836.
Thus, GCF of Fractions is 63/154836.Finally, GCF of Fractions for 378/414, 8631/2244 is 63/154836.