GCF of 493/214, 803/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 493/214, 803/419 i.e 1/89666 easily. The following is the detailed procedure to determine the greatest common factor of fractions 493/214, 803/419.
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 493/214,803/419?
Given fractions are 493/214,803/419
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 493/214,803/419, numerators are 493,803
Denominators are 214,419
The GCF of 493,803 is 1 .
LCM of 214,419 is 89666.
The greatest common factor of 493/214,803/419 = [GCF of 493,803]/[LCM of 214,419]= 1/89666
Therefore, the GCF of 493/214,803/419 is 1/89666.
To find the highest common factor of 493,803, we have to find the factors of both numbers and list the highest common factor.
The factors of 493 are 1, 17, 29, 493
The factors of 803 are 1, 11, 73, 803
The HCF of 493,803 is 1.
Lets's calculate GCF of 493,803
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 493,803 By Matching Biggest Common Factor Method
Now, list down the factors of 493
:1,17,29,493
Now, list down the factors of 803
:1,11,73,803
Greatest Common Factor
We found the factors 493,803 . The biggest common factor number is the GCF number.
So the greatest common factor 493,803 is 1.
Lets's calculate LCM of 214,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 89666
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/89666
Therefore, the GCF of Fractions 493/214,803/419 is 1/89666
Least Common Multiple of 214,419 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 214,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(214,419) x common factors =1 x 1 = 1
LCM(214,419) = ( 214 × 419 ) / 1
LCM(214,419) = 89666 / 1
LCM(214,419) = 89666
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FAQs on GCF of Fractions of 493/214, 803/419
1. What is the HCF of 493,803?
The HCF of 493,803 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 493/214, 803/419?
Answer: GCF of Numerators as per given numbers 493/214, 803/419 is
GCF of Numerators i.e. for 493,803 is 1
LCM of denominators i.e. for 214,419 is 89666.
Thus, GCF of Fractions is 1/89666.Finally, GCF of Fractions for 493/214, 803/419 is 1/89666.