GCF of 457/517, 7314/521
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 457/517, 7314/521 i.e 1/269357 easily. The following is the detailed procedure to determine the greatest common factor of fractions 457/517, 7314/521.
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 457/517,7314/521?
Given fractions are 457/517,7314/521
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 457/517,7314/521, numerators are 457,7314
Denominators are 517,521
The GCF of 457,7314 is 1 .
LCM of 517,521 is 269357.
The greatest common factor of 457/517,7314/521 = [GCF of 457,7314]/[LCM of 517,521]= 1/269357
Therefore, the GCF of 457/517,7314/521 is 1/269357.
To find the highest common factor of 457,7314, we have to find the factors of both numbers and list the highest common factor.
The factors of 457 are 1, 457
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 457,7314 is 1.
Lets's calculate GCF of 457,7314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 457,7314 By Matching Biggest Common Factor Method
Now, list down the factors of 457
:1,457
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 457,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 457,7314 is 1.
Lets's calculate LCM of 517,521
Given numbers has no common factors except 1. So, there LCM is their product i.e 269357
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/269357
Therefore, the GCF of Fractions 457/517,7314/521 is 1/269357
Least Common Multiple of 517,521 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 517,521 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(517,521) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(517,521) x common factors =1 x 1 = 1
LCM(517,521) = ( 517 × 521 ) / 1
LCM(517,521) = 269357 / 1
LCM(517,521) = 269357
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FAQs on GCF of Fractions of 457/517, 7314/521
1. What is the HCF of 457,7314?
The HCF of 457,7314 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 457/517, 7314/521?
Answer: GCF of Numerators as per given numbers 457/517, 7314/521 is
GCF of Numerators i.e. for 457,7314 is 1
LCM of denominators i.e. for 517,521 is 269357.
Thus, GCF of Fractions is 1/269357.Finally, GCF of Fractions for 457/517, 7314/521 is 1/269357.