GCF of 866/68, 378/31, 827/54
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 866/68, 378/31, 827/54 i.e 1/56916 easily. The following is the detailed procedure to determine the greatest common factor of fractions 866/68, 378/31, 827/54.
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 866/68,378/31,827/54?
Given fractions are 866/68,378/31,827/54
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 866/68,378/31,827/54, numerators are 866,378,827
Denominators are 68,31,54
The GCF of 866,378,827 is 1 .
LCM of 68,31,54 is 56916.
The greatest common factor of 866/68,378/31,827/54 = [GCF of 866,378,827]/[LCM of 68,31,54]= 1/56916
Therefore, the GCF of 866/68,378/31,827/54 is 1/56916.
To find the highest common factor of 866,378,827, we have to find the factors of both numbers and list the highest common factor.
The factors of 866 are 1, 2, 433, 866
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 827 are 1, 827
The HCF of 866,378,827 is 1.
Lets's calculate GCF of 866,378,827
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 866,378,827 By Matching Biggest Common Factor Method
Now, list down the factors of 866
:1,2,433,866
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 827
:1,827
Greatest Common Factor
We found the factors 866,378,827 . The biggest common factor number is the GCF number.
So the greatest common factor 866,378,827 is 1.
Lets's calculate LCM of 68,31,54
| 2 | 68, 31, 54 |
| 34, 31, 27 |
∴ So the LCM of the given numbers is 2 x 34 x 31 x 27 = 56916
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56916
Therefore, the GCF of Fractions 866/68,378/31,827/54 is 1/56916
Least Common Multiple of 68,31,54 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 68,31,54 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,31,54) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(68,31,54) x common factors =1 x 2 = 2
LCM(68,31,54) = ( 68 × 31 × 54 ) / 2
LCM(68,31,54) = 113832 / 2
LCM(68,31,54) = 56916
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FAQs on GCF of Fractions of 866/68, 378/31, 827/54
1. What is the HCF of 866,378,827?
The HCF of 866,378,827 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 866/68, 378/31, 827/54?
Answer: GCF of Numerators as per given numbers 866/68, 378/31, 827/54 is
GCF of Numerators i.e. for 866,378,827 is 1
LCM of denominators i.e. for 68,31,54 is 56916.
Thus, GCF of Fractions is 1/56916.Finally, GCF of Fractions for 866/68, 378/31, 827/54 is 1/56916.