GCF of 8034/342, 7070/2462
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8034/342, 7070/2462 i.e 2/421002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8034/342, 7070/2462.
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 8034/342,7070/2462?
Given fractions are 8034/342,7070/2462
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 8034/342,7070/2462, numerators are 8034,7070
Denominators are 342,2462
The GCF of 8034,7070 is 2 .
LCM of 342,2462 is 421002.
The greatest common factor of 8034/342,7070/2462 = [GCF of 8034,7070]/[LCM of 342,2462]= 2/421002
Therefore, the GCF of 8034/342,7070/2462 is 2/421002.
To find the highest common factor of 8034,7070, we have to find the factors of both numbers and list the highest common factor.
The factors of 8034 are 1, 2, 3, 6, 13, 26, 39, 78, 103, 206, 309, 618, 1339, 2678, 4017, 8034
The factors of 7070 are 1, 2, 5, 7, 10, 14, 35, 70, 101, 202, 505, 707, 1010, 1414, 3535, 7070
The HCF of 8034,7070 is 2.
Lets's calculate GCF of 8034,7070
| 2 | 8034, 7070 |
| 4017, 3535 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8034,7070 By Matching Biggest Common Factor Method
Now, list down the factors of 8034
:1,2,3,6,13,26,39,78,103,206,309,618,1339,2678,4017,8034
Now, list down the factors of 7070
:1,2,5,7,10,14,35,70,101,202,505,707,1010,1414,3535,7070
Greatest Common Factor
We found the factors 8034,7070 . The biggest common factor number is the GCF number.
So the greatest common factor 8034,7070 is 2.
Lets's calculate LCM of 342,2462
| 2 | 342, 2462 |
| 171, 1231 |
∴ So the LCM of the given numbers is 2 x 171 x 1231 = 421002
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/421002
Therefore, the GCF of Fractions 8034/342,7070/2462 is 2/421002
Least Common Multiple of 342,2462 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 342,2462 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,2462) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,2462) x common factors =2 x 1 = 2
LCM(342,2462) = ( 342 × 2462 ) / 2
LCM(342,2462) = 842004 / 2
LCM(342,2462) = 421002
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FAQs on GCF of Fractions of 8034/342, 7070/2462
1. What is the HCF of 8034,7070?
The HCF of 8034,7070 is 2
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 8034/342, 7070/2462?
Answer: GCF of Numerators as per given numbers 8034/342, 7070/2462 is
GCF of Numerators i.e. for 8034,7070 is 2
LCM of denominators i.e. for 342,2462 is 421002.
Thus, GCF of Fractions is 2/421002.Finally, GCF of Fractions for 8034/342, 7070/2462 is 2/421002.