GCF of 998/721, 8289/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 998/721, 8289/312 i.e 1/224952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 998/721, 8289/312.
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 998/721,8289/312?
Given fractions are 998/721,8289/312
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 998/721,8289/312, numerators are 998,8289
Denominators are 721,312
The GCF of 998,8289 is 1 .
LCM of 721,312 is 224952.
The greatest common factor of 998/721,8289/312 = [GCF of 998,8289]/[LCM of 721,312]= 1/224952
Therefore, the GCF of 998/721,8289/312 is 1/224952.
To find the highest common factor of 998,8289, we have to find the factors of both numbers and list the highest common factor.
The factors of 998 are 1, 2, 499, 998
The factors of 8289 are 1, 3, 9, 27, 307, 921, 2763, 8289
The HCF of 998,8289 is 1.
Lets's calculate GCF of 998,8289
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 998,8289 By Matching Biggest Common Factor Method
Now, list down the factors of 998
:1,2,499,998
Now, list down the factors of 8289
:1,3,9,27,307,921,2763,8289
Greatest Common Factor
We found the factors 998,8289 . The biggest common factor number is the GCF number.
So the greatest common factor 998,8289 is 1.
Lets's calculate LCM of 721,312
Given numbers has no common factors except 1. So, there LCM is their product i.e 224952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/224952
Therefore, the GCF of Fractions 998/721,8289/312 is 1/224952
Least Common Multiple of 721,312 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 721,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(721,312) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(721,312) x common factors =1 x 1 = 1
LCM(721,312) = ( 721 × 312 ) / 1
LCM(721,312) = 224952 / 1
LCM(721,312) = 224952
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FAQs on GCF of Fractions of 998/721, 8289/312
1. What is the HCF of 998,8289?
The HCF of 998,8289 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 998/721, 8289/312?
Answer: GCF of Numerators as per given numbers 998/721, 8289/312 is
GCF of Numerators i.e. for 998,8289 is 1
LCM of denominators i.e. for 721,312 is 224952.
Thus, GCF of Fractions is 1/224952.Finally, GCF of Fractions for 998/721, 8289/312 is 1/224952.