GCF of 327/769, 414/754
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 327/769, 414/754 i.e 3/579826 easily. The following is the detailed procedure to determine the greatest common factor of fractions 327/769, 414/754.
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 327/769,414/754?
Given fractions are 327/769,414/754
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 327/769,414/754, numerators are 327,414
Denominators are 769,754
The GCF of 327,414 is 3 .
LCM of 769,754 is 579826.
The greatest common factor of 327/769,414/754 = [GCF of 327,414]/[LCM of 769,754]= 3/579826
Therefore, the GCF of 327/769,414/754 is 3/579826.
To find the highest common factor of 327,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 327 are 1, 3, 109, 327
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 327,414 is 3.
Lets's calculate GCF of 327,414
| 3 | 327, 414 |
| 109, 138 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 327,414 By Matching Biggest Common Factor Method
Now, list down the factors of 327
:1,3,109,327
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 327,414 . The biggest common factor number is the GCF number.
So the greatest common factor 327,414 is 3.
Lets's calculate LCM of 769,754
Given numbers has no common factors except 1. So, there LCM is their product i.e 579826
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/579826
Therefore, the GCF of Fractions 327/769,414/754 is 3/579826
Least Common Multiple of 769,754 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 769,754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(769,754) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(769,754) x common factors =1 x 1 = 1
LCM(769,754) = ( 769 × 754 ) / 1
LCM(769,754) = 579826 / 1
LCM(769,754) = 579826
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FAQs on GCF of Fractions of 327/769, 414/754
1. What is the HCF of 327,414?
The HCF of 327,414 is 3
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 327/769, 414/754?
Answer: GCF of Numerators as per given numbers 327/769, 414/754 is
GCF of Numerators i.e. for 327,414 is 3
LCM of denominators i.e. for 769,754 is 579826.
Thus, GCF of Fractions is 3/579826.Finally, GCF of Fractions for 327/769, 414/754 is 3/579826.