Use our free GCF of Fractions Calculator tool to compute the GCF of 310/142, 719/162 i.e 1/11502 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/142, 719/162.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 310/142,719/162
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 310/142,719/162, numerators are 310,719
Denominators are 142,162
The GCF of 310,719 is 1 .
LCM of 142,162 is 11502.
The greatest common factor of 310/142,719/162 = [GCF of 310,719]/[LCM of 142,162]= 1/11502
Therefore, the GCF of 310/142,719/162 is 1/11502.
To find the highest common factor of 310,719, we have to find the factors of both numbers and list the highest common factor.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 719 are 1, 719
The HCF of 310,719 is 1.
Lets's calculate GCF of 310,719
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Now, list down the factors of 719
:1,719
Greatest Common Factor
We found the factors 310,719 . The biggest common factor number is the GCF number.
So the greatest common factor 310,719 is 1.
Lets's calculate LCM of 142,162
2 | 142, 162 |
71, 81 |
∴ So the LCM of the given numbers is 2 x 71 x 81 = 11502
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11502
Therefore, the GCF of Fractions 310/142,719/162 is 1/11502
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 142,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,162) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,162) x common factors =2 x 1 = 2
LCM(142,162) = ( 142 × 162 ) / 2
LCM(142,162) = 23004 / 2
LCM(142,162) = 11502
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 310,719?
The HCF of 310,719 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 310/142, 719/162?
Answer: GCF of Numerators as per given numbers 310/142, 719/162 is
GCF of Numerators i.e. for 310,719 is 1
LCM of denominators i.e. for 142,162 is 11502.
Thus, GCF of Fractions is 1/11502.Finally, GCF of Fractions for 310/142, 719/162 is 1/11502.