Use our free GCF of Fractions Calculator tool to compute the GCF of 32/54, 774/31, 217/608 i.e 1/508896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/54, 774/31, 217/608.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 32/54,774/31,217/608
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 32/54,774/31,217/608, numerators are 32,774,217
Denominators are 54,31,608
The GCF of 32,774,217 is 1 .
LCM of 54,31,608 is 508896.
The greatest common factor of 32/54,774/31,217/608 = [GCF of 32,774,217]/[LCM of 54,31,608]= 1/508896
Therefore, the GCF of 32/54,774/31,217/608 is 1/508896.
To find the highest common factor of 32,774,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The factors of 217 are 1, 7, 31, 217
The HCF of 32,774,217 is 1.
Lets's calculate GCF of 32,774,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 32,774,217 . The biggest common factor number is the GCF number.
So the greatest common factor 32,774,217 is 1.
Lets's calculate LCM of 54,31,608
2 | 54, 31, 608 |
27, 31, 304 |
∴ So the LCM of the given numbers is 2 x 27 x 31 x 304 = 508896
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/508896
Therefore, the GCF of Fractions 32/54,774/31,217/608 is 1/508896
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 54,31,608 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,31,608) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(54,31,608) x common factors =1 x 2 = 2
LCM(54,31,608) = ( 54 × 31 × 608 ) / 2
LCM(54,31,608) = 1017792 / 2
LCM(54,31,608) = 508896
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 32,774,217?
The HCF of 32,774,217 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 32/54, 774/31, 217/608?
Answer: GCF of Numerators as per given numbers 32/54, 774/31, 217/608 is
GCF of Numerators i.e. for 32,774,217 is 1
LCM of denominators i.e. for 54,31,608 is 508896.
Thus, GCF of Fractions is 1/508896.Finally, GCF of Fractions for 32/54, 774/31, 217/608 is 1/508896.