GCF of 642/115, 414/517
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 642/115, 414/517 i.e 6/59455 easily. The following is the detailed procedure to determine the greatest common factor of fractions 642/115, 414/517.
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 642/115,414/517?
Given fractions are 642/115,414/517
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 642/115,414/517, numerators are 642,414
Denominators are 115,517
The GCF of 642,414 is 6 .
LCM of 115,517 is 59455.
The greatest common factor of 642/115,414/517 = [GCF of 642,414]/[LCM of 115,517]= 6/59455
Therefore, the GCF of 642/115,414/517 is 6/59455.
To find the highest common factor of 642,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 642,414 is 6.
Lets's calculate GCF of 642,414
| 2 | 642, 414 |
| 3 | 321, 207 |
| 107, 69 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 642,414 By Matching Biggest Common Factor Method
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
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 642,414 . The biggest common factor number is the GCF number.
So the greatest common factor 642,414 is 6.
Lets's calculate LCM of 115,517
Given numbers has no common factors except 1. So, there LCM is their product i.e 59455
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/59455
Therefore, the GCF of Fractions 642/115,414/517 is 6/59455
Least Common Multiple of 115,517 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 115,517 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(115,517) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(115,517) x common factors =1 x 1 = 1
LCM(115,517) = ( 115 × 517 ) / 1
LCM(115,517) = 59455 / 1
LCM(115,517) = 59455
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FAQs on GCF of Fractions of 642/115, 414/517
1. What is the HCF of 642,414?
The HCF of 642,414 is 6
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 642/115, 414/517?
Answer: GCF of Numerators as per given numbers 642/115, 414/517 is
GCF of Numerators i.e. for 642,414 is 6
LCM of denominators i.e. for 115,517 is 59455.
Thus, GCF of Fractions is 6/59455.Finally, GCF of Fractions for 642/115, 414/517 is 6/59455.