Use our free GCF of Fractions Calculator tool to compute the GCF of 86/298, 35/616, 156/616 i.e 1/91784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/298, 35/616, 156/616.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 86/298,35/616,156/616
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 86/298,35/616,156/616, numerators are 86,35,156
Denominators are 298,616,616
The GCF of 86,35,156 is 1 .
LCM of 298,616,616 is 91784.
The greatest common factor of 86/298,35/616,156/616 = [GCF of 86,35,156]/[LCM of 298,616,616]= 1/91784
Therefore, the GCF of 86/298,35/616,156/616 is 1/91784.
To find the highest common factor of 86,35,156, 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 35 are 1, 5, 7, 35
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The HCF of 86,35,156 is 1.
Lets's calculate GCF of 86,35,156
∴ 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 35
:1,5,7,35
Now, list down the factors of 156
:1,2,3,4,6,12,13,26,39,52,78,156
Greatest Common Factor
We found the factors 86,35,156 . The biggest common factor number is the GCF number.
So the greatest common factor 86,35,156 is 1.
Lets's calculate LCM of 298,616,616
2 | 298, 616, 616 |
2 | 149, 308, 308 |
2 | 149, 154, 154 |
7 | 149, 77, 77 |
11 | 149, 11, 11 |
149, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 11 x 149 x 1 x 1 = 91784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/91784
Therefore, the GCF of Fractions 86/298,35/616,156/616 is 1/91784
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 298,616,616 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(298,616,616) = 2
common factors(in case of two or more numbers have common factors) = 616
GCF(298,616,616) x common factors =2 x 616 = 1232
LCM(298,616,616) = ( 298 × 616 × 616 ) / 1232
LCM(298,616,616) = 113077888 / 1232
LCM(298,616,616) = 91784
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 86,35,156?
The HCF of 86,35,156 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 86/298, 35/616, 156/616?
Answer: GCF of Numerators as per given numbers 86/298, 35/616, 156/616 is
GCF of Numerators i.e. for 86,35,156 is 1
LCM of denominators i.e. for 298,616,616 is 91784.
Thus, GCF of Fractions is 1/91784.Finally, GCF of Fractions for 86/298, 35/616, 156/616 is 1/91784.