GCF of 82/567, 31/980, 120/659
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/567, 31/980, 120/659 i.e 1/52311420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/567, 31/980, 120/659.
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 82/567,31/980,120/659?
Given fractions are 82/567,31/980,120/659
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 82/567,31/980,120/659, numerators are 82,31,120
Denominators are 567,980,659
The GCF of 82,31,120 is 1 .
LCM of 567,980,659 is 52311420.
The greatest common factor of 82/567,31/980,120/659 = [GCF of 82,31,120]/[LCM of 567,980,659]= 1/52311420
Therefore, the GCF of 82/567,31/980,120/659 is 1/52311420.
To find the highest common factor of 82,31,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 31 are 1, 31
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 82,31,120 is 1.
Lets's calculate GCF of 82,31,120
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 82,31,120 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 31
:1,31
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 82,31,120 . The biggest common factor number is the GCF number.
So the greatest common factor 82,31,120 is 1.
Lets's calculate LCM of 567,980,659
| 7 | 567, 980, 659 |
| 81, 140, 659 |
∴ So the LCM of the given numbers is 7 x 81 x 140 x 659 = 52311420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/52311420
Therefore, the GCF of Fractions 82/567,31/980,120/659 is 1/52311420
Least Common Multiple of 567,980,659 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 567,980,659 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(567,980,659) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(567,980,659) x common factors =1 x 7 = 7
LCM(567,980,659) = ( 567 × 980 × 659 ) / 7
LCM(567,980,659) = 366179940 / 7
LCM(567,980,659) = 52311420
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FAQs on GCF of Fractions of 82/567, 31/980, 120/659
1. What is the HCF of 82,31,120?
The HCF of 82,31,120 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 82/567, 31/980, 120/659?
Answer: GCF of Numerators as per given numbers 82/567, 31/980, 120/659 is
GCF of Numerators i.e. for 82,31,120 is 1
LCM of denominators i.e. for 567,980,659 is 52311420.
Thus, GCF of Fractions is 1/52311420.Finally, GCF of Fractions for 82/567, 31/980, 120/659 is 1/52311420.