GCF of 9750/142, 9870/6882
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9750/142, 9870/6882 i.e 30/488622 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9750/142, 9870/6882.
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 9750/142,9870/6882?
Given fractions are 9750/142,9870/6882
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 9750/142,9870/6882, numerators are 9750,9870
Denominators are 142,6882
The GCF of 9750,9870 is 30 .
LCM of 142,6882 is 488622.
The greatest common factor of 9750/142,9870/6882 = [GCF of 9750,9870]/[LCM of 142,6882]= 30/488622
Therefore, the GCF of 9750/142,9870/6882 is 30/488622.
To find the highest common factor of 9750,9870, we have to find the factors of both numbers and list the highest common factor.
The factors of 9750 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750
The factors of 9870 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 47, 70, 94, 105, 141, 210, 235, 282, 329, 470, 658, 705, 987, 1410, 1645, 1974, 3290, 4935, 9870
The HCF of 9750,9870 is 30.
Lets's calculate GCF of 9750,9870
| 2 | 9750, 9870 |
| 3 | 4875, 4935 |
| 5 | 1625, 1645 |
| 325, 329 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 9750,9870 By Matching Biggest Common Factor Method
Now, list down the factors of 9750
:1,2,3,5,6,10,13,15,25,26,30,39,50,65,75,78,125,130,150,195,250,325,375,390,650,750,975,1625,1950,3250,4875,9750
Now, list down the factors of 9870
:1,2,3,5,6,7,10,14,15,21,30,35,42,47,70,94,105,141,210,235,282,329,470,658,705,987,1410,1645,1974,3290,4935,9870
Greatest Common Factor
We found the factors 9750,9870 . The biggest common factor number is the GCF number.
So the greatest common factor 9750,9870 is 30.
Lets's calculate LCM of 142,6882
| 2 | 142, 6882 |
| 71, 3441 |
∴ So the LCM of the given numbers is 2 x 71 x 3441 = 488622
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/488622
Therefore, the GCF of Fractions 9750/142,9870/6882 is 30/488622
Least Common Multiple of 142,6882 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 142,6882 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,6882) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,6882) x common factors =2 x 1 = 2
LCM(142,6882) = ( 142 × 6882 ) / 2
LCM(142,6882) = 977244 / 2
LCM(142,6882) = 488622
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FAQs on GCF of Fractions of 9750/142, 9870/6882
1. What is the HCF of 9750,9870?
The HCF of 9750,9870 is 30
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 9750/142, 9870/6882?
Answer: GCF of Numerators as per given numbers 9750/142, 9870/6882 is
GCF of Numerators i.e. for 9750,9870 is 30
LCM of denominators i.e. for 142,6882 is 488622.
Thus, GCF of Fractions is 30/488622.Finally, GCF of Fractions for 9750/142, 9870/6882 is 30/488622.