GCF of 9828/859, 5740/5667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9828/859, 5740/5667 i.e 28/4867953 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9828/859, 5740/5667.
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 9828/859,5740/5667?
Given fractions are 9828/859,5740/5667
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 9828/859,5740/5667, numerators are 9828,5740
Denominators are 859,5667
The GCF of 9828,5740 is 28 .
LCM of 859,5667 is 4867953.
The greatest common factor of 9828/859,5740/5667 = [GCF of 9828,5740]/[LCM of 859,5667]= 28/4867953
Therefore, the GCF of 9828/859,5740/5667 is 28/4867953.
To find the highest common factor of 9828,5740, we have to find the factors of both numbers and list the highest common factor.
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 factors of 5740 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 41, 70, 82, 140, 164, 205, 287, 410, 574, 820, 1148, 1435, 2870, 5740
The HCF of 9828,5740 is 28.
Lets's calculate GCF of 9828,5740
| 2 | 9828, 5740 |
| 2 | 4914, 2870 |
| 7 | 2457, 1435 |
| 351, 205 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 9828,5740 By Matching Biggest Common Factor Method
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
Now, list down the factors of 5740
:1,2,4,5,7,10,14,20,28,35,41,70,82,140,164,205,287,410,574,820,1148,1435,2870,5740
Greatest Common Factor
We found the factors 9828,5740 . The biggest common factor number is the GCF number.
So the greatest common factor 9828,5740 is 28.
Lets's calculate LCM of 859,5667
Given numbers has no common factors except 1. So, there LCM is their product i.e 4867953
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/4867953
Therefore, the GCF of Fractions 9828/859,5740/5667 is 28/4867953
Least Common Multiple of 859,5667 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 859,5667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(859,5667) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(859,5667) x common factors =1 x 1 = 1
LCM(859,5667) = ( 859 × 5667 ) / 1
LCM(859,5667) = 4867953 / 1
LCM(859,5667) = 4867953
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FAQs on GCF of Fractions of 9828/859, 5740/5667
1. What is the HCF of 9828,5740?
The HCF of 9828,5740 is 28
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 9828/859, 5740/5667?
Answer: GCF of Numerators as per given numbers 9828/859, 5740/5667 is
GCF of Numerators i.e. for 9828,5740 is 28
LCM of denominators i.e. for 859,5667 is 4867953.
Thus, GCF of Fractions is 28/4867953.Finally, GCF of Fractions for 9828/859, 5740/5667 is 28/4867953.