GCF of 157/409, 8229/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 157/409, 8229/214 i.e 1/87526 easily. The following is the detailed procedure to determine the greatest common factor of fractions 157/409, 8229/214.
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 157/409,8229/214?
Given fractions are 157/409,8229/214
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 157/409,8229/214, numerators are 157,8229
Denominators are 409,214
The GCF of 157,8229 is 1 .
LCM of 409,214 is 87526.
The greatest common factor of 157/409,8229/214 = [GCF of 157,8229]/[LCM of 409,214]= 1/87526
Therefore, the GCF of 157/409,8229/214 is 1/87526.
To find the highest common factor of 157,8229, we have to find the factors of both numbers and list the highest common factor.
The factors of 157 are 1, 157
The factors of 8229 are 1, 3, 13, 39, 211, 633, 2743, 8229
The HCF of 157,8229 is 1.
Lets's calculate GCF of 157,8229
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 157,8229 By Matching Biggest Common Factor Method
Now, list down the factors of 157
:1,157
Now, list down the factors of 8229
:1,3,13,39,211,633,2743,8229
Greatest Common Factor
We found the factors 157,8229 . The biggest common factor number is the GCF number.
So the greatest common factor 157,8229 is 1.
Lets's calculate LCM of 409,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 87526
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/87526
Therefore, the GCF of Fractions 157/409,8229/214 is 1/87526
Least Common Multiple of 409,214 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 409,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,214) x common factors =1 x 1 = 1
LCM(409,214) = ( 409 × 214 ) / 1
LCM(409,214) = 87526 / 1
LCM(409,214) = 87526
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FAQs on GCF of Fractions of 157/409, 8229/214
1. What is the HCF of 157,8229?
The HCF of 157,8229 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 157/409, 8229/214?
Answer: GCF of Numerators as per given numbers 157/409, 8229/214 is
GCF of Numerators i.e. for 157,8229 is 1
LCM of denominators i.e. for 409,214 is 87526.
Thus, GCF of Fractions is 1/87526.Finally, GCF of Fractions for 157/409, 8229/214 is 1/87526.