GCF of 9195/208, 8460/5784
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9195/208, 8460/5784 i.e 15/150384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9195/208, 8460/5784.
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 9195/208,8460/5784?
Given fractions are 9195/208,8460/5784
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 9195/208,8460/5784, numerators are 9195,8460
Denominators are 208,5784
The GCF of 9195,8460 is 15 .
LCM of 208,5784 is 150384.
The greatest common factor of 9195/208,8460/5784 = [GCF of 9195,8460]/[LCM of 208,5784]= 15/150384
Therefore, the GCF of 9195/208,8460/5784 is 15/150384.
To find the highest common factor of 9195,8460, we have to find the factors of both numbers and list the highest common factor.
The factors of 9195 are 1, 3, 5, 15, 613, 1839, 3065, 9195
The factors of 8460 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 47, 60, 90, 94, 141, 180, 188, 235, 282, 423, 470, 564, 705, 846, 940, 1410, 1692, 2115, 2820, 4230, 8460
The HCF of 9195,8460 is 15.
Lets's calculate GCF of 9195,8460
| 3 | 9195, 8460 |
| 5 | 3065, 2820 |
| 613, 564 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 9195,8460 By Matching Biggest Common Factor Method
Now, list down the factors of 9195
:1,3,5,15,613,1839,3065,9195
Now, list down the factors of 8460
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,47,60,90,94,141,180,188,235,282,423,470,564,705,846,940,1410,1692,2115,2820,4230,8460
Greatest Common Factor
We found the factors 9195,8460 . The biggest common factor number is the GCF number.
So the greatest common factor 9195,8460 is 15.
Lets's calculate LCM of 208,5784
| 2 | 208, 5784 |
| 2 | 104, 2892 |
| 2 | 52, 1446 |
| 26, 723 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 26 x 723 = 150384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/150384
Therefore, the GCF of Fractions 9195/208,8460/5784 is 15/150384
Least Common Multiple of 208,5784 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 208,5784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,5784) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(208,5784) x common factors =8 x 1 = 8
LCM(208,5784) = ( 208 × 5784 ) / 8
LCM(208,5784) = 1203072 / 8
LCM(208,5784) = 150384
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FAQs on GCF of Fractions of 9195/208, 8460/5784
1. What is the HCF of 9195,8460?
The HCF of 9195,8460 is 15
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 9195/208, 8460/5784?
Answer: GCF of Numerators as per given numbers 9195/208, 8460/5784 is
GCF of Numerators i.e. for 9195,8460 is 15
LCM of denominators i.e. for 208,5784 is 150384.
Thus, GCF of Fractions is 15/150384.Finally, GCF of Fractions for 9195/208, 8460/5784 is 15/150384.