GCF of 9666/414, 9219/980
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9666/414, 9219/980 i.e 3/202860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9666/414, 9219/980.
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 9666/414,9219/980?
Given fractions are 9666/414,9219/980
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 9666/414,9219/980, numerators are 9666,9219
Denominators are 414,980
The GCF of 9666,9219 is 3 .
LCM of 414,980 is 202860.
The greatest common factor of 9666/414,9219/980 = [GCF of 9666,9219]/[LCM of 414,980]= 3/202860
Therefore, the GCF of 9666/414,9219/980 is 3/202860.
To find the highest common factor of 9666,9219, we have to find the factors of both numbers and list the highest common factor.
The factors of 9666 are 1, 2, 3, 6, 9, 18, 27, 54, 179, 358, 537, 1074, 1611, 3222, 4833, 9666
The factors of 9219 are 1, 3, 7, 21, 439, 1317, 3073, 9219
The HCF of 9666,9219 is 3.
Lets's calculate GCF of 9666,9219
| 3 | 9666, 9219 |
| 3222, 3073 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9666,9219 By Matching Biggest Common Factor Method
Now, list down the factors of 9666
:1,2,3,6,9,18,27,54,179,358,537,1074,1611,3222,4833,9666
Now, list down the factors of 9219
:1,3,7,21,439,1317,3073,9219
Greatest Common Factor
We found the factors 9666,9219 . The biggest common factor number is the GCF number.
So the greatest common factor 9666,9219 is 3.
Lets's calculate LCM of 414,980
| 2 | 414, 980 |
| 207, 490 |
∴ So the LCM of the given numbers is 2 x 207 x 490 = 202860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/202860
Therefore, the GCF of Fractions 9666/414,9219/980 is 3/202860
Least Common Multiple of 414,980 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 414,980 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,980) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,980) x common factors =2 x 1 = 2
LCM(414,980) = ( 414 × 980 ) / 2
LCM(414,980) = 405720 / 2
LCM(414,980) = 202860
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 9666/414, 9219/980
1. What is the HCF of 9666,9219?
The HCF of 9666,9219 is 3
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 9666/414, 9219/980?
Answer: GCF of Numerators as per given numbers 9666/414, 9219/980 is
GCF of Numerators i.e. for 9666,9219 is 3
LCM of denominators i.e. for 414,980 is 202860.
Thus, GCF of Fractions is 3/202860.Finally, GCF of Fractions for 9666/414, 9219/980 is 3/202860.