Use our free GCF of Fractions Calculator tool to compute the GCF of 113/315, 684/474 i.e 1/49770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 113/315, 684/474.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 113/315,684/474
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 113/315,684/474, numerators are 113,684
Denominators are 315,474
The GCF of 113,684 is 1 .
LCM of 315,474 is 49770.
The greatest common factor of 113/315,684/474 = [GCF of 113,684]/[LCM of 315,474]= 1/49770
Therefore, the GCF of 113/315,684/474 is 1/49770.
To find the highest common factor of 113,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 113 are 1, 113
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 113,684 is 1.
Lets's calculate GCF of 113,684
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 113
:1,113
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 113,684 . The biggest common factor number is the GCF number.
So the greatest common factor 113,684 is 1.
Lets's calculate LCM of 315,474
3 | 315, 474 |
105, 158 |
∴ So the LCM of the given numbers is 3 x 105 x 158 = 49770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/49770
Therefore, the GCF of Fractions 113/315,684/474 is 1/49770
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 315,474 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(315,474) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(315,474) x common factors =3 x 1 = 3
LCM(315,474) = ( 315 × 474 ) / 3
LCM(315,474) = 149310 / 3
LCM(315,474) = 49770
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 113,684?
The HCF of 113,684 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 113/315, 684/474?
Answer: GCF of Numerators as per given numbers 113/315, 684/474 is
GCF of Numerators i.e. for 113,684 is 1
LCM of denominators i.e. for 315,474 is 49770.
Thus, GCF of Fractions is 1/49770.Finally, GCF of Fractions for 113/315, 684/474 is 1/49770.