GCF of 7854/128, 9469/3230
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7854/128, 9469/3230 i.e 17/206720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7854/128, 9469/3230.
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 7854/128,9469/3230?
Given fractions are 7854/128,9469/3230
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 7854/128,9469/3230, numerators are 7854,9469
Denominators are 128,3230
The GCF of 7854,9469 is 17 .
LCM of 128,3230 is 206720.
The greatest common factor of 7854/128,9469/3230 = [GCF of 7854,9469]/[LCM of 128,3230]= 17/206720
Therefore, the GCF of 7854/128,9469/3230 is 17/206720.
To find the highest common factor of 7854,9469, we have to find the factors of both numbers and list the highest common factor.
The factors of 7854 are 1, 2, 3, 6, 7, 11, 14, 17, 21, 22, 33, 34, 42, 51, 66, 77, 102, 119, 154, 187, 231, 238, 357, 374, 462, 561, 714, 1122, 1309, 2618, 3927, 7854
The factors of 9469 are 1, 17, 557, 9469
The HCF of 7854,9469 is 17.
Lets's calculate GCF of 7854,9469
| 17 | 7854, 9469 |
| 462, 557 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 7854,9469 By Matching Biggest Common Factor Method
Now, list down the factors of 7854
:1,2,3,6,7,11,14,17,21,22,33,34,42,51,66,77,102,119,154,187,231,238,357,374,462,561,714,1122,1309,2618,3927,7854
Now, list down the factors of 9469
:1,17,557,9469
Greatest Common Factor
We found the factors 7854,9469 . The biggest common factor number is the GCF number.
So the greatest common factor 7854,9469 is 17.
Lets's calculate LCM of 128,3230
| 2 | 128, 3230 |
| 64, 1615 |
∴ So the LCM of the given numbers is 2 x 64 x 1615 = 206720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/206720
Therefore, the GCF of Fractions 7854/128,9469/3230 is 17/206720
Least Common Multiple of 128,3230 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 128,3230 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(128,3230) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(128,3230) x common factors =2 x 1 = 2
LCM(128,3230) = ( 128 × 3230 ) / 2
LCM(128,3230) = 413440 / 2
LCM(128,3230) = 206720
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FAQs on GCF of Fractions of 7854/128, 9469/3230
1. What is the HCF of 7854,9469?
The HCF of 7854,9469 is 17
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 7854/128, 9469/3230?
Answer: GCF of Numerators as per given numbers 7854/128, 9469/3230 is
GCF of Numerators i.e. for 7854,9469 is 17
LCM of denominators i.e. for 128,3230 is 206720.
Thus, GCF of Fractions is 17/206720.Finally, GCF of Fractions for 7854/128, 9469/3230 is 17/206720.