GCF of 43/57, 161/34, 713/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 43/57, 161/34, 713/414 i.e 1/133722 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/57, 161/34, 713/414.
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 43/57,161/34,713/414?
Given fractions are 43/57,161/34,713/414
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 43/57,161/34,713/414, numerators are 43,161,713
Denominators are 57,34,414
The GCF of 43,161,713 is 1 .
LCM of 57,34,414 is 133722.
The greatest common factor of 43/57,161/34,713/414 = [GCF of 43,161,713]/[LCM of 57,34,414]= 1/133722
Therefore, the GCF of 43/57,161/34,713/414 is 1/133722.
To find the highest common factor of 43,161,713, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 161 are 1, 7, 23, 161
The factors of 713 are 1, 23, 31, 713
The HCF of 43,161,713 is 1.
Lets's calculate GCF of 43,161,713
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 43,161,713 By Matching Biggest Common Factor Method
Now, list down the factors of 43
:1,43
Now, list down the factors of 161
:1,7,23,161
Now, list down the factors of 713
:1,23,31,713
Greatest Common Factor
We found the factors 43,161,713 . The biggest common factor number is the GCF number.
So the greatest common factor 43,161,713 is 1.
Lets's calculate LCM of 57,34,414
| 2 | 57, 34, 414 |
| 3 | 57, 17, 207 |
| 19, 17, 69 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 17 x 69 = 133722
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/133722
Therefore, the GCF of Fractions 43/57,161/34,713/414 is 1/133722
Least Common Multiple of 57,34,414 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 57,34,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,34,414) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(57,34,414) x common factors =1 x 6 = 6
LCM(57,34,414) = ( 57 × 34 × 414 ) / 6
LCM(57,34,414) = 802332 / 6
LCM(57,34,414) = 133722
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FAQs on GCF of Fractions of 43/57, 161/34, 713/414
1. What is the HCF of 43,161,713?
The HCF of 43,161,713 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 43/57, 161/34, 713/414?
Answer: GCF of Numerators as per given numbers 43/57, 161/34, 713/414 is
GCF of Numerators i.e. for 43,161,713 is 1
LCM of denominators i.e. for 57,34,414 is 133722.
Thus, GCF of Fractions is 1/133722.Finally, GCF of Fractions for 43/57, 161/34, 713/414 is 1/133722.