GCF of 820/71, 782/73, 314/67
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 820/71, 782/73, 314/67 i.e 2/347261 easily. The following is the detailed procedure to determine the greatest common factor of fractions 820/71, 782/73, 314/67.
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 820/71,782/73,314/67?
Given fractions are 820/71,782/73,314/67
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 820/71,782/73,314/67, numerators are 820,782,314
Denominators are 71,73,67
The GCF of 820,782,314 is 2 .
LCM of 71,73,67 is 347261.
The greatest common factor of 820/71,782/73,314/67 = [GCF of 820,782,314]/[LCM of 71,73,67]= 2/347261
Therefore, the GCF of 820/71,782/73,314/67 is 2/347261.
To find the highest common factor of 820,782,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The factors of 314 are 1, 2, 157, 314
The HCF of 820,782,314 is 2.
Lets's calculate GCF of 820,782,314
| 2 | 820, 782, 314 |
| 410, 391, 157 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 820,782,314 By Matching Biggest Common Factor Method
Now, list down the factors of 820
:1,2,4,5,10,20,41,82,164,205,410,820
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 820,782,314 . The biggest common factor number is the GCF number.
So the greatest common factor 820,782,314 is 2.
Lets's calculate LCM of 71,73,67
Given numbers has no common factors except 1. So, there LCM is their product i.e 347261
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/347261
Therefore, the GCF of Fractions 820/71,782/73,314/67 is 2/347261
Least Common Multiple of 71,73,67 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 71,73,67 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,73,67) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,73,67) x common factors =1 x 1 = 1
LCM(71,73,67) = ( 71 × 73 × 67 ) / 1
LCM(71,73,67) = 347261 / 1
LCM(71,73,67) = 347261
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FAQs on GCF of Fractions of 820/71, 782/73, 314/67
1. What is the HCF of 820,782,314?
The HCF of 820,782,314 is 2
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 820/71, 782/73, 314/67?
Answer: GCF of Numerators as per given numbers 820/71, 782/73, 314/67 is
GCF of Numerators i.e. for 820,782,314 is 2
LCM of denominators i.e. for 71,73,67 is 347261.
Thus, GCF of Fractions is 2/347261.Finally, GCF of Fractions for 820/71, 782/73, 314/67 is 2/347261.