Use our free GCF of Fractions Calculator tool to compute the GCF of 56/103, 34/614, 132/643 i.e 2/40664606 easily. The following is the detailed procedure to determine the greatest common factor of fractions 56/103, 34/614, 132/643.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 56/103,34/614,132/643
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 56/103,34/614,132/643, numerators are 56,34,132
Denominators are 103,614,643
The GCF of 56,34,132 is 2 .
LCM of 103,614,643 is 40664606.
The greatest common factor of 56/103,34/614,132/643 = [GCF of 56,34,132]/[LCM of 103,614,643]= 2/40664606
Therefore, the GCF of 56/103,34/614,132/643 is 2/40664606.
To find the highest common factor of 56,34,132, we have to find the factors of both numbers and list the highest common factor.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The factors of 34 are 1, 2, 17, 34
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The HCF of 56,34,132 is 2.
Lets's calculate GCF of 56,34,132
2 | 56, 34, 132 |
28, 17, 66 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Greatest Common Factor
We found the factors 56,34,132 . The biggest common factor number is the GCF number.
So the greatest common factor 56,34,132 is 2.
Lets's calculate LCM of 103,614,643
Given numbers has no common factors except 1. So, there LCM is their product i.e 40664606
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/40664606
Therefore, the GCF of Fractions 56/103,34/614,132/643 is 2/40664606
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 103,614,643 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(103,614,643) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(103,614,643) x common factors =1 x 1 = 1
LCM(103,614,643) = ( 103 × 614 × 643 ) / 1
LCM(103,614,643) = 40664606 / 1
LCM(103,614,643) = 40664606
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 56,34,132?
The HCF of 56,34,132 is 2
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 56/103, 34/614, 132/643?
Answer: GCF of Numerators as per given numbers 56/103, 34/614, 132/643 is
GCF of Numerators i.e. for 56,34,132 is 2
LCM of denominators i.e. for 103,614,643 is 40664606.
Thus, GCF of Fractions is 2/40664606.Finally, GCF of Fractions for 56/103, 34/614, 132/643 is 2/40664606.