Use our free GCF of Fractions Calculator tool to compute the GCF of 86/512, 71/172, 294/430 i.e 1/110080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/512, 71/172, 294/430.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 86/512,71/172,294/430
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 86/512,71/172,294/430, numerators are 86,71,294
Denominators are 512,172,430
The GCF of 86,71,294 is 1 .
LCM of 512,172,430 is 110080.
The greatest common factor of 86/512,71/172,294/430 = [GCF of 86,71,294]/[LCM of 512,172,430]= 1/110080
Therefore, the GCF of 86/512,71/172,294/430 is 1/110080.
To find the highest common factor of 86,71,294, we have to find the factors of both numbers and list the highest common factor.
The factors of 86 are 1, 2, 43, 86
The factors of 71 are 1, 71
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 86,71,294 is 1.
Lets's calculate GCF of 86,71,294
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 71
:1,71
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 86,71,294 . The biggest common factor number is the GCF number.
So the greatest common factor 86,71,294 is 1.
Lets's calculate LCM of 512,172,430
2 | 512, 172, 430 |
2 | 256, 86, 215 |
43 | 128, 43, 215 |
128, 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 43 x 128 x 1 x 5 = 110080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/110080
Therefore, the GCF of Fractions 86/512,71/172,294/430 is 1/110080
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 512,172,430 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,172,430) = 2
common factors(in case of two or more numbers have common factors) = 172
GCF(512,172,430) x common factors =2 x 172 = 344
LCM(512,172,430) = ( 512 × 172 × 430 ) / 344
LCM(512,172,430) = 37867520 / 344
LCM(512,172,430) = 110080
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 86,71,294?
The HCF of 86,71,294 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 86/512, 71/172, 294/430?
Answer: GCF of Numerators as per given numbers 86/512, 71/172, 294/430 is
GCF of Numerators i.e. for 86,71,294 is 1
LCM of denominators i.e. for 512,172,430 is 110080.
Thus, GCF of Fractions is 1/110080.Finally, GCF of Fractions for 86/512, 71/172, 294/430 is 1/110080.