GCF of 827/251, 160/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 827/251, 160/214 i.e 1/53714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 827/251, 160/214.
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 827/251,160/214?
Given fractions are 827/251,160/214
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 827/251,160/214, numerators are 827,160
Denominators are 251,214
The GCF of 827,160 is 1 .
LCM of 251,214 is 53714.
The greatest common factor of 827/251,160/214 = [GCF of 827,160]/[LCM of 251,214]= 1/53714
Therefore, the GCF of 827/251,160/214 is 1/53714.
To find the highest common factor of 827,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 827 are 1, 827
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 827,160 is 1.
Lets's calculate GCF of 827,160
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 827,160 By Matching Biggest Common Factor Method
Now, list down the factors of 827
:1,827
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 827,160 . The biggest common factor number is the GCF number.
So the greatest common factor 827,160 is 1.
Lets's calculate LCM of 251,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 53714
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/53714
Therefore, the GCF of Fractions 827/251,160/214 is 1/53714
Least Common Multiple of 251,214 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 251,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(251,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(251,214) x common factors =1 x 1 = 1
LCM(251,214) = ( 251 × 214 ) / 1
LCM(251,214) = 53714 / 1
LCM(251,214) = 53714
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FAQs on GCF of Fractions of 827/251, 160/214
1. What is the HCF of 827,160?
The HCF of 827,160 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 827/251, 160/214?
Answer: GCF of Numerators as per given numbers 827/251, 160/214 is
GCF of Numerators i.e. for 827,160 is 1
LCM of denominators i.e. for 251,214 is 53714.
Thus, GCF of Fractions is 1/53714.Finally, GCF of Fractions for 827/251, 160/214 is 1/53714.