GCF of 3/82, 8/11, 7/71, 31/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/82, 8/11, 7/71, 31/419 i.e 1/26833598 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/82, 8/11, 7/71, 31/419.
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 3/82,8/11,7/71,31/419?
Given fractions are 3/82,8/11,7/71,31/419
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 3/82,8/11,7/71,31/419, numerators are 3,8,7,31
Denominators are 82,11,71,419
The GCF of 3,8,7,31 is 1 .
LCM of 82,11,71,419 is 26833598.
The greatest common factor of 3/82,8/11,7/71,31/419 = [GCF of 3,8,7,31]/[LCM of 82,11,71,419]= 1/26833598
Therefore, the GCF of 3/82,8/11,7/71,31/419 is 1/26833598.
To find the highest common factor of 3,8,7,31, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 8 are 1, 2, 4, 8
The factors of 7 are 1, 7
The factors of 31 are 1, 31
The HCF of 3,8,7,31 is 1.
Lets's calculate GCF of 3,8,7,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,8,7,31 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 7
:1,7
Now, list down the factors of 31
:1,31
Greatest Common Factor
We found the factors 3,8,7,31 . The biggest common factor number is the GCF number.
So the greatest common factor 3,8,7,31 is 1.
Lets's calculate LCM of 82,11,71,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 26833598
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26833598
Therefore, the GCF of Fractions 3/82,8/11,7/71,31/419 is 1/26833598
Least Common Multiple of 82,11,71,419 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 82,11,71,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,11,71,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(82,11,71,419) x common factors =1 x 1 = 1
LCM(82,11,71,419) = ( 82 × 11 × 71 × 419 ) / 1
LCM(82,11,71,419) = 26833598 / 1
LCM(82,11,71,419) = 26833598
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3/82, 8/11, 7/71, 31/419
1. What is the HCF of 3,8,7,31?
The HCF of 3,8,7,31 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 3/82, 8/11, 7/71, 31/419?
Answer: GCF of Numerators as per given numbers 3/82, 8/11, 7/71, 31/419 is
GCF of Numerators i.e. for 3,8,7,31 is 1
LCM of denominators i.e. for 82,11,71,419 is 26833598.
Thus, GCF of Fractions is 1/26833598.Finally, GCF of Fractions for 3/82, 8/11, 7/71, 31/419 is 1/26833598.