GCF of 7038/294, 6314/3963
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7038/294, 6314/3963 i.e 2/388374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7038/294, 6314/3963.
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 7038/294,6314/3963?
Given fractions are 7038/294,6314/3963
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 7038/294,6314/3963, numerators are 7038,6314
Denominators are 294,3963
The GCF of 7038,6314 is 2 .
LCM of 294,3963 is 388374.
The greatest common factor of 7038/294,6314/3963 = [GCF of 7038,6314]/[LCM of 294,3963]= 2/388374
Therefore, the GCF of 7038/294,6314/3963 is 2/388374.
To find the highest common factor of 7038,6314, we have to find the factors of both numbers and list the highest common factor.
The factors of 7038 are 1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519, 7038
The factors of 6314 are 1, 2, 7, 11, 14, 22, 41, 77, 82, 154, 287, 451, 574, 902, 3157, 6314
The HCF of 7038,6314 is 2.
Lets's calculate GCF of 7038,6314
| 2 | 7038, 6314 |
| 3519, 3157 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7038,6314 By Matching Biggest Common Factor Method
Now, list down the factors of 7038
:1,2,3,6,9,17,18,23,34,46,51,69,102,138,153,207,306,391,414,782,1173,2346,3519,7038
Now, list down the factors of 6314
:1,2,7,11,14,22,41,77,82,154,287,451,574,902,3157,6314
Greatest Common Factor
We found the factors 7038,6314 . The biggest common factor number is the GCF number.
So the greatest common factor 7038,6314 is 2.
Lets's calculate LCM of 294,3963
| 3 | 294, 3963 |
| 98, 1321 |
∴ So the LCM of the given numbers is 3 x 98 x 1321 = 388374
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/388374
Therefore, the GCF of Fractions 7038/294,6314/3963 is 2/388374
Least Common Multiple of 294,3963 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 294,3963 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(294,3963) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(294,3963) x common factors =3 x 1 = 3
LCM(294,3963) = ( 294 × 3963 ) / 3
LCM(294,3963) = 1165122 / 3
LCM(294,3963) = 388374
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FAQs on GCF of Fractions of 7038/294, 6314/3963
1. What is the HCF of 7038,6314?
The HCF of 7038,6314 is 2
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 7038/294, 6314/3963?
Answer: GCF of Numerators as per given numbers 7038/294, 6314/3963 is
GCF of Numerators i.e. for 7038,6314 is 2
LCM of denominators i.e. for 294,3963 is 388374.
Thus, GCF of Fractions is 2/388374.Finally, GCF of Fractions for 7038/294, 6314/3963 is 2/388374.