GCF of 871/302, 509/982
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 871/302, 509/982 i.e 1/148282 easily. The following is the detailed procedure to determine the greatest common factor of fractions 871/302, 509/982.
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 871/302,509/982?
Given fractions are 871/302,509/982
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 871/302,509/982, numerators are 871,509
Denominators are 302,982
The GCF of 871,509 is 1 .
LCM of 302,982 is 148282.
The greatest common factor of 871/302,509/982 = [GCF of 871,509]/[LCM of 302,982]= 1/148282
Therefore, the GCF of 871/302,509/982 is 1/148282.
To find the highest common factor of 871,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 871 are 1, 13, 67, 871
The factors of 509 are 1, 509
The HCF of 871,509 is 1.
Lets's calculate GCF of 871,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 871,509 By Matching Biggest Common Factor Method
Now, list down the factors of 871
:1,13,67,871
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 871,509 . The biggest common factor number is the GCF number.
So the greatest common factor 871,509 is 1.
Lets's calculate LCM of 302,982
| 2 | 302, 982 |
| 151, 491 |
∴ So the LCM of the given numbers is 2 x 151 x 491 = 148282
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/148282
Therefore, the GCF of Fractions 871/302,509/982 is 1/148282
Least Common Multiple of 302,982 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 302,982 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(302,982) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(302,982) x common factors =2 x 1 = 2
LCM(302,982) = ( 302 × 982 ) / 2
LCM(302,982) = 296564 / 2
LCM(302,982) = 148282
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FAQs on GCF of Fractions of 871/302, 509/982
1. What is the HCF of 871,509?
The HCF of 871,509 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 871/302, 509/982?
Answer: GCF of Numerators as per given numbers 871/302, 509/982 is
GCF of Numerators i.e. for 871,509 is 1
LCM of denominators i.e. for 302,982 is 148282.
Thus, GCF of Fractions is 1/148282.Finally, GCF of Fractions for 871/302, 509/982 is 1/148282.