GCF of 8130/978, 6775/128
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8130/978, 6775/128 i.e 1355/62592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8130/978, 6775/128.
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 8130/978,6775/128?
Given fractions are 8130/978,6775/128
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 8130/978,6775/128, numerators are 8130,6775
Denominators are 978,128
The GCF of 8130,6775 is 1355 .
LCM of 978,128 is 62592.
The greatest common factor of 8130/978,6775/128 = [GCF of 8130,6775]/[LCM of 978,128]= 1355/62592
Therefore, the GCF of 8130/978,6775/128 is 1355/62592.
To find the highest common factor of 8130,6775, we have to find the factors of both numbers and list the highest common factor.
The factors of 8130 are 1, 2, 3, 5, 6, 10, 15, 30, 271, 542, 813, 1355, 1626, 2710, 4065, 8130
The factors of 6775 are 1, 5, 25, 271, 1355, 6775
The HCF of 8130,6775 is 1355.
Lets's calculate GCF of 8130,6775
| 5 | 8130, 6775 |
| 271 | 1626, 1355 |
| 6, 5 |
∴ So the GCF of the given numbers is 5 x 271 = 1355
Greatest Common Factor of 8130,6775 By Matching Biggest Common Factor Method
Now, list down the factors of 8130
:1,2,3,5,6,10,15,30,271,542,813,1355,1626,2710,4065,8130
Now, list down the factors of 6775
:1,5,25,271,1355,6775
Greatest Common Factor
We found the factors 8130,6775 . The biggest common factor number is the GCF number.
So the greatest common factor 8130,6775 is 1355.
Lets's calculate LCM of 978,128
| 2 | 978, 128 |
| 489, 64 |
∴ So the LCM of the given numbers is 2 x 489 x 64 = 62592
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1355/62592
Therefore, the GCF of Fractions 8130/978,6775/128 is 1355/62592
Least Common Multiple of 978,128 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 978,128 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,128) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(978,128) x common factors =2 x 1 = 2
LCM(978,128) = ( 978 × 128 ) / 2
LCM(978,128) = 125184 / 2
LCM(978,128) = 62592
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FAQs on GCF of Fractions of 8130/978, 6775/128
1. What is the HCF of 8130,6775?
The HCF of 8130,6775 is 1355
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 8130/978, 6775/128?
Answer: GCF of Numerators as per given numbers 8130/978, 6775/128 is
GCF of Numerators i.e. for 8130,6775 is 1355
LCM of denominators i.e. for 978,128 is 62592.
Thus, GCF of Fractions is 1355/62592.Finally, GCF of Fractions for 8130/978, 6775/128 is 1355/62592.