Use our free GCF of Fractions Calculator tool to compute the GCF of 112/238, 653/119 i.e 1/238 easily. The following is the detailed procedure to determine the greatest common factor of fractions 112/238, 653/119.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 112/238,653/119
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 112/238,653/119, numerators are 112,653
Denominators are 238,119
The GCF of 112,653 is 1 .
LCM of 238,119 is 238.
The greatest common factor of 112/238,653/119 = [GCF of 112,653]/[LCM of 238,119]= 1/238
Therefore, the GCF of 112/238,653/119 is 1/238.
To find the highest common factor of 112,653, we have to find the factors of both numbers and list the highest common factor.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The factors of 653 are 1, 653
The HCF of 112,653 is 1.
Lets's calculate GCF of 112,653
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Now, list down the factors of 653
:1,653
Greatest Common Factor
We found the factors 112,653 . The biggest common factor number is the GCF number.
So the greatest common factor 112,653 is 1.
Lets's calculate LCM of 238,119
7 | 238, 119 |
17 | 34, 17 |
2, 1 |
∴ So the LCM of the given numbers is 7 x 17 x 2 x 1 = 238
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/238
Therefore, the GCF of Fractions 112/238,653/119 is 1/238
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 238,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(238,119) = 119
common factors(in case of two or more numbers have common factors) = 1
GCF(238,119) x common factors =119 x 1 = 119
LCM(238,119) = ( 238 × 119 ) / 119
LCM(238,119) = 28322 / 119
LCM(238,119) = 238
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 112,653?
The HCF of 112,653 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 112/238, 653/119?
Answer: GCF of Numerators as per given numbers 112/238, 653/119 is
GCF of Numerators i.e. for 112,653 is 1
LCM of denominators i.e. for 238,119 is 238.
Thus, GCF of Fractions is 1/238.Finally, GCF of Fractions for 112/238, 653/119 is 1/238.