GCF of 68/854, 75/320, 206/722
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/854, 75/320, 206/722 i.e 1/49327040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/854, 75/320, 206/722.
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 68/854,75/320,206/722?
Given fractions are 68/854,75/320,206/722
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 68/854,75/320,206/722, numerators are 68,75,206
Denominators are 854,320,722
The GCF of 68,75,206 is 1 .
LCM of 854,320,722 is 49327040.
The greatest common factor of 68/854,75/320,206/722 = [GCF of 68,75,206]/[LCM of 854,320,722]= 1/49327040
Therefore, the GCF of 68/854,75/320,206/722 is 1/49327040.
To find the highest common factor of 68,75,206, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 206 are 1, 2, 103, 206
The HCF of 68,75,206 is 1.
Lets's calculate GCF of 68,75,206
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 68,75,206 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 206
:1,2,103,206
Greatest Common Factor
We found the factors 68,75,206 . The biggest common factor number is the GCF number.
So the greatest common factor 68,75,206 is 1.
Lets's calculate LCM of 854,320,722
| 2 | 854, 320, 722 |
| 427, 160, 361 |
∴ So the LCM of the given numbers is 2 x 427 x 160 x 361 = 49327040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/49327040
Therefore, the GCF of Fractions 68/854,75/320,206/722 is 1/49327040
Least Common Multiple of 854,320,722 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 854,320,722 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,320,722) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(854,320,722) x common factors =2 x 2 = 4
LCM(854,320,722) = ( 854 × 320 × 722 ) / 4
LCM(854,320,722) = 197308160 / 4
LCM(854,320,722) = 49327040
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FAQs on GCF of Fractions of 68/854, 75/320, 206/722
1. What is the HCF of 68,75,206?
The HCF of 68,75,206 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 68/854, 75/320, 206/722?
Answer: GCF of Numerators as per given numbers 68/854, 75/320, 206/722 is
GCF of Numerators i.e. for 68,75,206 is 1
LCM of denominators i.e. for 854,320,722 is 49327040.
Thus, GCF of Fractions is 1/49327040.Finally, GCF of Fractions for 68/854, 75/320, 206/722 is 1/49327040.