GCF of 613/51, 561/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 613/51, 561/419 i.e 1/21369 easily. The following is the detailed procedure to determine the greatest common factor of fractions 613/51, 561/419.
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 613/51,561/419?
Given fractions are 613/51,561/419
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 613/51,561/419, numerators are 613,561
Denominators are 51,419
The GCF of 613,561 is 1 .
LCM of 51,419 is 21369.
The greatest common factor of 613/51,561/419 = [GCF of 613,561]/[LCM of 51,419]= 1/21369
Therefore, the GCF of 613/51,561/419 is 1/21369.
To find the highest common factor of 613,561, we have to find the factors of both numbers and list the highest common factor.
The factors of 613 are 1, 613
The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561
The HCF of 613,561 is 1.
Lets's calculate GCF of 613,561
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 613,561 By Matching Biggest Common Factor Method
Now, list down the factors of 613
:1,613
Now, list down the factors of 561
:1,3,11,17,33,51,187,561
Greatest Common Factor
We found the factors 613,561 . The biggest common factor number is the GCF number.
So the greatest common factor 613,561 is 1.
Lets's calculate LCM of 51,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 21369
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21369
Therefore, the GCF of Fractions 613/51,561/419 is 1/21369
Least Common Multiple of 51,419 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 51,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,419) x common factors =1 x 1 = 1
LCM(51,419) = ( 51 × 419 ) / 1
LCM(51,419) = 21369 / 1
LCM(51,419) = 21369
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 613/51, 561/419
1. What is the HCF of 613,561?
The HCF of 613,561 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 613/51, 561/419?
Answer: GCF of Numerators as per given numbers 613/51, 561/419 is
GCF of Numerators i.e. for 613,561 is 1
LCM of denominators i.e. for 51,419 is 21369.
Thus, GCF of Fractions is 1/21369.Finally, GCF of Fractions for 613/51, 561/419 is 1/21369.