GCF of 316/771, 405/234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 316/771, 405/234 i.e 1/60138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 316/771, 405/234.
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 316/771,405/234?
Given fractions are 316/771,405/234
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 316/771,405/234, numerators are 316,405
Denominators are 771,234
The GCF of 316,405 is 1 .
LCM of 771,234 is 60138.
The greatest common factor of 316/771,405/234 = [GCF of 316,405]/[LCM of 771,234]= 1/60138
Therefore, the GCF of 316/771,405/234 is 1/60138.
To find the highest common factor of 316,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 316 are 1, 2, 4, 79, 158, 316
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 316,405 is 1.
Lets's calculate GCF of 316,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 316,405 By Matching Biggest Common Factor Method
Now, list down the factors of 316
:1,2,4,79,158,316
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 316,405 . The biggest common factor number is the GCF number.
So the greatest common factor 316,405 is 1.
Lets's calculate LCM of 771,234
| 3 | 771, 234 |
| 257, 78 |
∴ So the LCM of the given numbers is 3 x 257 x 78 = 60138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/60138
Therefore, the GCF of Fractions 316/771,405/234 is 1/60138
Least Common Multiple of 771,234 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 771,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(771,234) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(771,234) x common factors =3 x 1 = 3
LCM(771,234) = ( 771 × 234 ) / 3
LCM(771,234) = 180414 / 3
LCM(771,234) = 60138
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FAQs on GCF of Fractions of 316/771, 405/234
1. What is the HCF of 316,405?
The HCF of 316,405 is 1
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 316/771, 405/234?
Answer: GCF of Numerators as per given numbers 316/771, 405/234 is
GCF of Numerators i.e. for 316,405 is 1
LCM of denominators i.e. for 771,234 is 60138.
Thus, GCF of Fractions is 1/60138.Finally, GCF of Fractions for 316/771, 405/234 is 1/60138.