GCF of 8/91, 68/46, 85/784, 194/812
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/91, 68/46, 85/784, 194/812 i.e 1/6798064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/91, 68/46, 85/784, 194/812.
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 8/91,68/46,85/784,194/812?
Given fractions are 8/91,68/46,85/784,194/812
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 8/91,68/46,85/784,194/812, numerators are 8,68,85,194
Denominators are 91,46,784,812
The GCF of 8,68,85,194 is 1 .
LCM of 91,46,784,812 is 6798064.
The greatest common factor of 8/91,68/46,85/784,194/812 = [GCF of 8,68,85,194]/[LCM of 91,46,784,812]= 1/6798064
Therefore, the GCF of 8/91,68/46,85/784,194/812 is 1/6798064.
To find the highest common factor of 8,68,85,194, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 85 are 1, 5, 17, 85
The factors of 194 are 1, 2, 97, 194
The HCF of 8,68,85,194 is 1.
Lets's calculate GCF of 8,68,85,194
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8,68,85,194 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 85
:1,5,17,85
Now, list down the factors of 194
:1,2,97,194
Greatest Common Factor
We found the factors 8,68,85,194 . The biggest common factor number is the GCF number.
So the greatest common factor 8,68,85,194 is 1.
Lets's calculate LCM of 91,46,784,812
| 2 | 91, 46, 784, 812 |
| 2 | 91, 23, 392, 406 |
| 7 | 91, 23, 196, 203 |
| 13, 23, 28, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 13 x 23 x 28 x 29 = 6798064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6798064
Therefore, the GCF of Fractions 8/91,68/46,85/784,194/812 is 1/6798064
Least Common Multiple of 91,46,784,812 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 91,46,784,812 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(91,46,784,812) = 1
common factors(in case of two or more numbers have common factors) = 392
GCF(91,46,784,812) x common factors =1 x 392 = 392
LCM(91,46,784,812) = ( 91 × 46 × 784 × 812 ) / 392
LCM(91,46,784,812) = 2664841088 / 392
LCM(91,46,784,812) = 6798064
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 8/91, 68/46, 85/784, 194/812
1. What is the HCF of 8,68,85,194?
The HCF of 8,68,85,194 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 8/91, 68/46, 85/784, 194/812?
Answer: GCF of Numerators as per given numbers 8/91, 68/46, 85/784, 194/812 is
GCF of Numerators i.e. for 8,68,85,194 is 1
LCM of denominators i.e. for 91,46,784,812 is 6798064.
Thus, GCF of Fractions is 1/6798064.Finally, GCF of Fractions for 8/91, 68/46, 85/784, 194/812 is 1/6798064.