GCF of 517/82, 646/362
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 517/82, 646/362 i.e 1/14842 easily. The following is the detailed procedure to determine the greatest common factor of fractions 517/82, 646/362.
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 517/82,646/362?
Given fractions are 517/82,646/362
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 517/82,646/362, numerators are 517,646
Denominators are 82,362
The GCF of 517,646 is 1 .
LCM of 82,362 is 14842.
The greatest common factor of 517/82,646/362 = [GCF of 517,646]/[LCM of 82,362]= 1/14842
Therefore, the GCF of 517/82,646/362 is 1/14842.
To find the highest common factor of 517,646, we have to find the factors of both numbers and list the highest common factor.
The factors of 517 are 1, 11, 47, 517
The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646
The HCF of 517,646 is 1.
Lets's calculate GCF of 517,646
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 517,646 By Matching Biggest Common Factor Method
Now, list down the factors of 517
:1,11,47,517
Now, list down the factors of 646
:1,2,17,19,34,38,323,646
Greatest Common Factor
We found the factors 517,646 . The biggest common factor number is the GCF number.
So the greatest common factor 517,646 is 1.
Lets's calculate LCM of 82,362
| 2 | 82, 362 |
| 41, 181 |
∴ So the LCM of the given numbers is 2 x 41 x 181 = 14842
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14842
Therefore, the GCF of Fractions 517/82,646/362 is 1/14842
Least Common Multiple of 82,362 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 82,362 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,362) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,362) x common factors =2 x 1 = 2
LCM(82,362) = ( 82 × 362 ) / 2
LCM(82,362) = 29684 / 2
LCM(82,362) = 14842
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FAQs on GCF of Fractions of 517/82, 646/362
1. What is the HCF of 517,646?
The HCF of 517,646 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 517/82, 646/362?
Answer: GCF of Numerators as per given numbers 517/82, 646/362 is
GCF of Numerators i.e. for 517,646 is 1
LCM of denominators i.e. for 82,362 is 14842.
Thus, GCF of Fractions is 1/14842.Finally, GCF of Fractions for 517/82, 646/362 is 1/14842.