GCF of 7824/242, 2838/7034
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7824/242, 2838/7034 i.e 6/851114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7824/242, 2838/7034.
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 7824/242,2838/7034?
Given fractions are 7824/242,2838/7034
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 7824/242,2838/7034, numerators are 7824,2838
Denominators are 242,7034
The GCF of 7824,2838 is 6 .
LCM of 242,7034 is 851114.
The greatest common factor of 7824/242,2838/7034 = [GCF of 7824,2838]/[LCM of 242,7034]= 6/851114
Therefore, the GCF of 7824/242,2838/7034 is 6/851114.
To find the highest common factor of 7824,2838, we have to find the factors of both numbers and list the highest common factor.
The factors of 7824 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824
The factors of 2838 are 1, 2, 3, 6, 11, 22, 33, 43, 66, 86, 129, 258, 473, 946, 1419, 2838
The HCF of 7824,2838 is 6.
Lets's calculate GCF of 7824,2838
| 2 | 7824, 2838 |
| 3 | 3912, 1419 |
| 1304, 473 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7824,2838 By Matching Biggest Common Factor Method
Now, list down the factors of 7824
:1,2,3,4,6,8,12,16,24,48,163,326,489,652,978,1304,1956,2608,3912,7824
Now, list down the factors of 2838
:1,2,3,6,11,22,33,43,66,86,129,258,473,946,1419,2838
Greatest Common Factor
We found the factors 7824,2838 . The biggest common factor number is the GCF number.
So the greatest common factor 7824,2838 is 6.
Lets's calculate LCM of 242,7034
| 2 | 242, 7034 |
| 121, 3517 |
∴ So the LCM of the given numbers is 2 x 121 x 3517 = 851114
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/851114
Therefore, the GCF of Fractions 7824/242,2838/7034 is 6/851114
Least Common Multiple of 242,7034 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 242,7034 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(242,7034) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(242,7034) x common factors =2 x 1 = 2
LCM(242,7034) = ( 242 × 7034 ) / 2
LCM(242,7034) = 1702228 / 2
LCM(242,7034) = 851114
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FAQs on GCF of Fractions of 7824/242, 2838/7034
1. What is the HCF of 7824,2838?
The HCF of 7824,2838 is 6
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 7824/242, 2838/7034?
Answer: GCF of Numerators as per given numbers 7824/242, 2838/7034 is
GCF of Numerators i.e. for 7824,2838 is 6
LCM of denominators i.e. for 242,7034 is 851114.
Thus, GCF of Fractions is 6/851114.Finally, GCF of Fractions for 7824/242, 2838/7034 is 6/851114.