GCF of 6/80, 27/31, 76/200, 743/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6/80, 27/31, 76/200, 743/120 i.e 1/37200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6/80, 27/31, 76/200, 743/120.
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 6/80,27/31,76/200,743/120?
Given fractions are 6/80,27/31,76/200,743/120
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 6/80,27/31,76/200,743/120, numerators are 6,27,76,743
Denominators are 80,31,200,120
The GCF of 6,27,76,743 is 1 .
LCM of 80,31,200,120 is 37200.
The greatest common factor of 6/80,27/31,76/200,743/120 = [GCF of 6,27,76,743]/[LCM of 80,31,200,120]= 1/37200
Therefore, the GCF of 6/80,27/31,76/200,743/120 is 1/37200.
To find the highest common factor of 6,27,76,743, we have to find the factors of both numbers and list the highest common factor.
The factors of 6 are 1, 2, 3, 6
The factors of 27 are 1, 3, 9, 27
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 743 are 1, 743
The HCF of 6,27,76,743 is 1.
Lets's calculate GCF of 6,27,76,743
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6,27,76,743 By Matching Biggest Common Factor Method
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 743
:1,743
Greatest Common Factor
We found the factors 6,27,76,743 . The biggest common factor number is the GCF number.
So the greatest common factor 6,27,76,743 is 1.
Lets's calculate LCM of 80,31,200,120
| 2 | 80, 31, 200, 120 |
| 2 | 40, 31, 100, 60 |
| 2 | 20, 31, 50, 30 |
| 5 | 10, 31, 25, 15 |
| 2, 31, 5, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 2 x 31 x 5 x 3 = 37200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37200
Therefore, the GCF of Fractions 6/80,27/31,76/200,743/120 is 1/37200
Least Common Multiple of 80,31,200,120 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 80,31,200,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(80,31,200,120) = 1
common factors(in case of two or more numbers have common factors) = 1600
GCF(80,31,200,120) x common factors =1 x 1600 = 1600
LCM(80,31,200,120) = ( 80 × 31 × 200 × 120 ) / 1600
LCM(80,31,200,120) = 59520000 / 1600
LCM(80,31,200,120) = 37200
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 6/80, 27/31, 76/200, 743/120
1. What is the HCF of 6,27,76,743?
The HCF of 6,27,76,743 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 6/80, 27/31, 76/200, 743/120?
Answer: GCF of Numerators as per given numbers 6/80, 27/31, 76/200, 743/120 is
GCF of Numerators i.e. for 6,27,76,743 is 1
LCM of denominators i.e. for 80,31,200,120 is 37200.
Thus, GCF of Fractions is 1/37200.Finally, GCF of Fractions for 6/80, 27/31, 76/200, 743/120 is 1/37200.