GCF of 329/409, 238/784
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 329/409, 238/784 i.e 7/320656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 329/409, 238/784.
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 329/409,238/784?
Given fractions are 329/409,238/784
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 329/409,238/784, numerators are 329,238
Denominators are 409,784
The GCF of 329,238 is 7 .
LCM of 409,784 is 320656.
The greatest common factor of 329/409,238/784 = [GCF of 329,238]/[LCM of 409,784]= 7/320656
Therefore, the GCF of 329/409,238/784 is 7/320656.
To find the highest common factor of 329,238, we have to find the factors of both numbers and list the highest common factor.
The factors of 329 are 1, 7, 47, 329
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The HCF of 329,238 is 7.
Lets's calculate GCF of 329,238
| 7 | 329, 238 |
| 47, 34 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 329,238 By Matching Biggest Common Factor Method
Now, list down the factors of 329
:1,7,47,329
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Greatest Common Factor
We found the factors 329,238 . The biggest common factor number is the GCF number.
So the greatest common factor 329,238 is 7.
Lets's calculate LCM of 409,784
Given numbers has no common factors except 1. So, there LCM is their product i.e 320656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/320656
Therefore, the GCF of Fractions 329/409,238/784 is 7/320656
Least Common Multiple of 409,784 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 409,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,784) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,784) x common factors =1 x 1 = 1
LCM(409,784) = ( 409 × 784 ) / 1
LCM(409,784) = 320656 / 1
LCM(409,784) = 320656
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FAQs on GCF of Fractions of 329/409, 238/784
1. What is the HCF of 329,238?
The HCF of 329,238 is 7
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 329/409, 238/784?
Answer: GCF of Numerators as per given numbers 329/409, 238/784 is
GCF of Numerators i.e. for 329,238 is 7
LCM of denominators i.e. for 409,784 is 320656.
Thus, GCF of Fractions is 7/320656.Finally, GCF of Fractions for 329/409, 238/784 is 7/320656.