GCF of 6870/375, 7842/2657
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6870/375, 7842/2657 i.e 6/996375 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6870/375, 7842/2657.
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 6870/375,7842/2657?
Given fractions are 6870/375,7842/2657
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 6870/375,7842/2657, numerators are 6870,7842
Denominators are 375,2657
The GCF of 6870,7842 is 6 .
LCM of 375,2657 is 996375.
The greatest common factor of 6870/375,7842/2657 = [GCF of 6870,7842]/[LCM of 375,2657]= 6/996375
Therefore, the GCF of 6870/375,7842/2657 is 6/996375.
To find the highest common factor of 6870,7842, we have to find the factors of both numbers and list the highest common factor.
The factors of 6870 are 1, 2, 3, 5, 6, 10, 15, 30, 229, 458, 687, 1145, 1374, 2290, 3435, 6870
The factors of 7842 are 1, 2, 3, 6, 1307, 2614, 3921, 7842
The HCF of 6870,7842 is 6.
Lets's calculate GCF of 6870,7842
| 2 | 6870, 7842 |
| 3 | 3435, 3921 |
| 1145, 1307 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 6870,7842 By Matching Biggest Common Factor Method
Now, list down the factors of 6870
:1,2,3,5,6,10,15,30,229,458,687,1145,1374,2290,3435,6870
Now, list down the factors of 7842
:1,2,3,6,1307,2614,3921,7842
Greatest Common Factor
We found the factors 6870,7842 . The biggest common factor number is the GCF number.
So the greatest common factor 6870,7842 is 6.
Lets's calculate LCM of 375,2657
Given numbers has no common factors except 1. So, there LCM is their product i.e 996375
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/996375
Therefore, the GCF of Fractions 6870/375,7842/2657 is 6/996375
Least Common Multiple of 375,2657 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 375,2657 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(375,2657) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(375,2657) x common factors =1 x 1 = 1
LCM(375,2657) = ( 375 × 2657 ) / 1
LCM(375,2657) = 996375 / 1
LCM(375,2657) = 996375
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FAQs on GCF of Fractions of 6870/375, 7842/2657
1. What is the HCF of 6870,7842?
The HCF of 6870,7842 is 6
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 6870/375, 7842/2657?
Answer: GCF of Numerators as per given numbers 6870/375, 7842/2657 is
GCF of Numerators i.e. for 6870,7842 is 6
LCM of denominators i.e. for 375,2657 is 996375.
Thus, GCF of Fractions is 6/996375.Finally, GCF of Fractions for 6870/375, 7842/2657 is 6/996375.