GCF of 491/117, 414/262
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 491/117, 414/262 i.e 1/30654 easily. The following is the detailed procedure to determine the greatest common factor of fractions 491/117, 414/262.
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 491/117,414/262?
Given fractions are 491/117,414/262
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 491/117,414/262, numerators are 491,414
Denominators are 117,262
The GCF of 491,414 is 1 .
LCM of 117,262 is 30654.
The greatest common factor of 491/117,414/262 = [GCF of 491,414]/[LCM of 117,262]= 1/30654
Therefore, the GCF of 491/117,414/262 is 1/30654.
To find the highest common factor of 491,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 491 are 1, 491
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 491,414 is 1.
Lets's calculate GCF of 491,414
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 491,414 By Matching Biggest Common Factor Method
Now, list down the factors of 491
:1,491
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 491,414 . The biggest common factor number is the GCF number.
So the greatest common factor 491,414 is 1.
Lets's calculate LCM of 117,262
Given numbers has no common factors except 1. So, there LCM is their product i.e 30654
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30654
Therefore, the GCF of Fractions 491/117,414/262 is 1/30654
Least Common Multiple of 117,262 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 117,262 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(117,262) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(117,262) x common factors =1 x 1 = 1
LCM(117,262) = ( 117 × 262 ) / 1
LCM(117,262) = 30654 / 1
LCM(117,262) = 30654
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 491/117, 414/262
1. What is the HCF of 491,414?
The HCF of 491,414 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 491/117, 414/262?
Answer: GCF of Numerators as per given numbers 491/117, 414/262 is
GCF of Numerators i.e. for 491,414 is 1
LCM of denominators i.e. for 117,262 is 30654.
Thus, GCF of Fractions is 1/30654.Finally, GCF of Fractions for 491/117, 414/262 is 1/30654.