GCF of 4234/831, 9828/309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4234/831, 9828/309 i.e 2/85593 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4234/831, 9828/309.
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 4234/831,9828/309?
Given fractions are 4234/831,9828/309
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 4234/831,9828/309, numerators are 4234,9828
Denominators are 831,309
The GCF of 4234,9828 is 2 .
LCM of 831,309 is 85593.
The greatest common factor of 4234/831,9828/309 = [GCF of 4234,9828]/[LCM of 831,309]= 2/85593
Therefore, the GCF of 4234/831,9828/309 is 2/85593.
To find the highest common factor of 4234,9828, we have to find the factors of both numbers and list the highest common factor.
The factors of 4234 are 1, 2, 29, 58, 73, 146, 2117, 4234
The factors of 9828 are 1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 26, 27, 28, 36, 39, 42, 52, 54, 63, 78, 84, 91, 108, 117, 126, 156, 182, 189, 234, 252, 273, 351, 364, 378, 468, 546, 702, 756, 819, 1092, 1404, 1638, 2457, 3276, 4914, 9828
The HCF of 4234,9828 is 2.
Lets's calculate GCF of 4234,9828
| 2 | 4234, 9828 |
| 2117, 4914 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 4234,9828 By Matching Biggest Common Factor Method
Now, list down the factors of 4234
:1,2,29,58,73,146,2117,4234
Now, list down the factors of 9828
:1,2,3,4,6,7,9,12,13,14,18,21,26,27,28,36,39,42,52,54,63,78,84,91,108,117,126,156,182,189,234,252,273,351,364,378,468,546,702,756,819,1092,1404,1638,2457,3276,4914,9828
Greatest Common Factor
We found the factors 4234,9828 . The biggest common factor number is the GCF number.
So the greatest common factor 4234,9828 is 2.
Lets's calculate LCM of 831,309
| 3 | 831, 309 |
| 277, 103 |
∴ So the LCM of the given numbers is 3 x 277 x 103 = 85593
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/85593
Therefore, the GCF of Fractions 4234/831,9828/309 is 2/85593
Least Common Multiple of 831,309 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 831,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(831,309) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(831,309) x common factors =3 x 1 = 3
LCM(831,309) = ( 831 × 309 ) / 3
LCM(831,309) = 256779 / 3
LCM(831,309) = 85593
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FAQs on GCF of Fractions of 4234/831, 9828/309
1. What is the HCF of 4234,9828?
The HCF of 4234,9828 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 4234/831, 9828/309?
Answer: GCF of Numerators as per given numbers 4234/831, 9828/309 is
GCF of Numerators i.e. for 4234,9828 is 2
LCM of denominators i.e. for 831,309 is 85593.
Thus, GCF of Fractions is 2/85593.Finally, GCF of Fractions for 4234/831, 9828/309 is 2/85593.