GCF of 8/31, 10/64, 79/128, 789/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/31, 10/64, 79/128, 789/217 i.e 1/27776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/31, 10/64, 79/128, 789/217.
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 8/31,10/64,79/128,789/217?
Given fractions are 8/31,10/64,79/128,789/217
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 8/31,10/64,79/128,789/217, numerators are 8,10,79,789
Denominators are 31,64,128,217
The GCF of 8,10,79,789 is 1 .
LCM of 31,64,128,217 is 27776.
The greatest common factor of 8/31,10/64,79/128,789/217 = [GCF of 8,10,79,789]/[LCM of 31,64,128,217]= 1/27776
Therefore, the GCF of 8/31,10/64,79/128,789/217 is 1/27776.
To find the highest common factor of 8,10,79,789, 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 10 are 1, 2, 5, 10
The factors of 79 are 1, 79
The factors of 789 are 1, 3, 263, 789
The HCF of 8,10,79,789 is 1.
Lets's calculate GCF of 8,10,79,789
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8,10,79,789 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 79
:1,79
Now, list down the factors of 789
:1,3,263,789
Greatest Common Factor
We found the factors 8,10,79,789 . The biggest common factor number is the GCF number.
So the greatest common factor 8,10,79,789 is 1.
Lets's calculate LCM of 31,64,128,217
| 2 | 31, 64, 128, 217 |
| 2 | 31, 32, 64, 217 |
| 2 | 31, 16, 32, 217 |
| 2 | 31, 8, 16, 217 |
| 2 | 31, 4, 8, 217 |
| 2 | 31, 2, 4, 217 |
| 31 | 31, 1, 2, 217 |
| 1, 1, 2, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 31 x 1 x 1 x 2 x 7 = 27776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27776
Therefore, the GCF of Fractions 8/31,10/64,79/128,789/217 is 1/27776
Least Common Multiple of 31,64,128,217 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 31,64,128,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,64,128,217) = 1
common factors(in case of two or more numbers have common factors) = 1984
GCF(31,64,128,217) x common factors =1 x 1984 = 1984
LCM(31,64,128,217) = ( 31 × 64 × 128 × 217 ) / 1984
LCM(31,64,128,217) = 55107584 / 1984
LCM(31,64,128,217) = 27776
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 8/31, 10/64, 79/128, 789/217
1. What is the HCF of 8,10,79,789?
The HCF of 8,10,79,789 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 8/31, 10/64, 79/128, 789/217?
Answer: GCF of Numerators as per given numbers 8/31, 10/64, 79/128, 789/217 is
GCF of Numerators i.e. for 8,10,79,789 is 1
LCM of denominators i.e. for 31,64,128,217 is 27776.
Thus, GCF of Fractions is 1/27776.Finally, GCF of Fractions for 8/31, 10/64, 79/128, 789/217 is 1/27776.