GCF of 7138/704, 3430/9071
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7138/704, 3430/9071 i.e 2/6385984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7138/704, 3430/9071.
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 7138/704,3430/9071?
Given fractions are 7138/704,3430/9071
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 7138/704,3430/9071, numerators are 7138,3430
Denominators are 704,9071
The GCF of 7138,3430 is 2 .
LCM of 704,9071 is 6385984.
The greatest common factor of 7138/704,3430/9071 = [GCF of 7138,3430]/[LCM of 704,9071]= 2/6385984
Therefore, the GCF of 7138/704,3430/9071 is 2/6385984.
To find the highest common factor of 7138,3430, we have to find the factors of both numbers and list the highest common factor.
The factors of 7138 are 1, 2, 43, 83, 86, 166, 3569, 7138
The factors of 3430 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715, 3430
The HCF of 7138,3430 is 2.
Lets's calculate GCF of 7138,3430
| 2 | 7138, 3430 |
| 3569, 1715 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7138,3430 By Matching Biggest Common Factor Method
Now, list down the factors of 7138
:1,2,43,83,86,166,3569,7138
Now, list down the factors of 3430
:1,2,5,7,10,14,35,49,70,98,245,343,490,686,1715,3430
Greatest Common Factor
We found the factors 7138,3430 . The biggest common factor number is the GCF number.
So the greatest common factor 7138,3430 is 2.
Lets's calculate LCM of 704,9071
Given numbers has no common factors except 1. So, there LCM is their product i.e 6385984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6385984
Therefore, the GCF of Fractions 7138/704,3430/9071 is 2/6385984
Least Common Multiple of 704,9071 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 704,9071 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(704,9071) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(704,9071) x common factors =1 x 1 = 1
LCM(704,9071) = ( 704 × 9071 ) / 1
LCM(704,9071) = 6385984 / 1
LCM(704,9071) = 6385984
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FAQs on GCF of Fractions of 7138/704, 3430/9071
1. What is the HCF of 7138,3430?
The HCF of 7138,3430 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 7138/704, 3430/9071?
Answer: GCF of Numerators as per given numbers 7138/704, 3430/9071 is
GCF of Numerators i.e. for 7138,3430 is 2
LCM of denominators i.e. for 704,9071 is 6385984.
Thus, GCF of Fractions is 2/6385984.Finally, GCF of Fractions for 7138/704, 3430/9071 is 2/6385984.