GCF of 6986/143, 9450/275
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6986/143, 9450/275 i.e 14/3575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6986/143, 9450/275.
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 6986/143,9450/275?
Given fractions are 6986/143,9450/275
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 6986/143,9450/275, numerators are 6986,9450
Denominators are 143,275
The GCF of 6986,9450 is 14 .
LCM of 143,275 is 3575.
The greatest common factor of 6986/143,9450/275 = [GCF of 6986,9450]/[LCM of 143,275]= 14/3575
Therefore, the GCF of 6986/143,9450/275 is 14/3575.
To find the highest common factor of 6986,9450, we have to find the factors of both numbers and list the highest common factor.
The factors of 6986 are 1, 2, 7, 14, 499, 998, 3493, 6986
The factors of 9450 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725, 9450
The HCF of 6986,9450 is 14.
Lets's calculate GCF of 6986,9450
| 2 | 6986, 9450 |
| 7 | 3493, 4725 |
| 499, 675 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 6986,9450 By Matching Biggest Common Factor Method
Now, list down the factors of 6986
:1,2,7,14,499,998,3493,6986
Now, list down the factors of 9450
:1,2,3,5,6,7,9,10,14,15,18,21,25,27,30,35,42,45,50,54,63,70,75,90,105,126,135,150,175,189,210,225,270,315,350,378,450,525,630,675,945,1050,1350,1575,1890,3150,4725,9450
Greatest Common Factor
We found the factors 6986,9450 . The biggest common factor number is the GCF number.
So the greatest common factor 6986,9450 is 14.
Lets's calculate LCM of 143,275
| 11 | 143, 275 |
| 13, 25 |
∴ So the LCM of the given numbers is 11 x 13 x 25 = 3575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/3575
Therefore, the GCF of Fractions 6986/143,9450/275 is 14/3575
Least Common Multiple of 143,275 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 143,275 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(143,275) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(143,275) x common factors =11 x 1 = 11
LCM(143,275) = ( 143 × 275 ) / 11
LCM(143,275) = 39325 / 11
LCM(143,275) = 3575
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FAQs on GCF of Fractions of 6986/143, 9450/275
1. What is the HCF of 6986,9450?
The HCF of 6986,9450 is 14
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 6986/143, 9450/275?
Answer: GCF of Numerators as per given numbers 6986/143, 9450/275 is
GCF of Numerators i.e. for 6986,9450 is 14
LCM of denominators i.e. for 143,275 is 3575.
Thus, GCF of Fractions is 14/3575.Finally, GCF of Fractions for 6986/143, 9450/275 is 14/3575.