GCF of 917/81, 861/108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 917/81, 861/108 i.e 7/324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 917/81, 861/108.
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 917/81,861/108?
Given fractions are 917/81,861/108
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 917/81,861/108, numerators are 917,861
Denominators are 81,108
The GCF of 917,861 is 7 .
LCM of 81,108 is 324.
The greatest common factor of 917/81,861/108 = [GCF of 917,861]/[LCM of 81,108]= 7/324
Therefore, the GCF of 917/81,861/108 is 7/324.
To find the highest common factor of 917,861, we have to find the factors of both numbers and list the highest common factor.
The factors of 917 are 1, 7, 131, 917
The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861
The HCF of 917,861 is 7.
Lets's calculate GCF of 917,861
| 7 | 917, 861 |
| 131, 123 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 917,861 By Matching Biggest Common Factor Method
Now, list down the factors of 917
:1,7,131,917
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Greatest Common Factor
We found the factors 917,861 . The biggest common factor number is the GCF number.
So the greatest common factor 917,861 is 7.
Lets's calculate LCM of 81,108
| 3 | 81, 108 |
| 3 | 27, 36 |
| 3 | 9, 12 |
| 3, 4 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 3 x 4 = 324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/324
Therefore, the GCF of Fractions 917/81,861/108 is 7/324
Least Common Multiple of 81,108 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 81,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,108) = 27
common factors(in case of two or more numbers have common factors) = 1
GCF(81,108) x common factors =27 x 1 = 27
LCM(81,108) = ( 81 × 108 ) / 27
LCM(81,108) = 8748 / 27
LCM(81,108) = 324
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 917/81, 861/108
1. What is the HCF of 917,861?
The HCF of 917,861 is 7
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 917/81, 861/108?
Answer: GCF of Numerators as per given numbers 917/81, 861/108 is
GCF of Numerators i.e. for 917,861 is 7
LCM of denominators i.e. for 81,108 is 324.
Thus, GCF of Fractions is 7/324.Finally, GCF of Fractions for 917/81, 861/108 is 7/324.