Use our free GCF of Fractions Calculator tool to compute the GCF of 473/420, 653/115 i.e 1/9660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 473/420, 653/115.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 473/420,653/115
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 473/420,653/115, numerators are 473,653
Denominators are 420,115
The GCF of 473,653 is 1 .
LCM of 420,115 is 9660.
The greatest common factor of 473/420,653/115 = [GCF of 473,653]/[LCM of 420,115]= 1/9660
Therefore, the GCF of 473/420,653/115 is 1/9660.
To find the highest common factor of 473,653, we have to find the factors of both numbers and list the highest common factor.
The factors of 473 are 1, 11, 43, 473
The factors of 653 are 1, 653
The HCF of 473,653 is 1.
Lets's calculate GCF of 473,653
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 473
:1,11,43,473
Now, list down the factors of 653
:1,653
Greatest Common Factor
We found the factors 473,653 . The biggest common factor number is the GCF number.
So the greatest common factor 473,653 is 1.
Lets's calculate LCM of 420,115
5 | 420, 115 |
84, 23 |
∴ So the LCM of the given numbers is 5 x 84 x 23 = 9660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9660
Therefore, the GCF of Fractions 473/420,653/115 is 1/9660
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 420,115 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,115) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(420,115) x common factors =5 x 1 = 5
LCM(420,115) = ( 420 × 115 ) / 5
LCM(420,115) = 48300 / 5
LCM(420,115) = 9660
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 473,653?
The HCF of 473,653 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 473/420, 653/115?
Answer: GCF of Numerators as per given numbers 473/420, 653/115 is
GCF of Numerators i.e. for 473,653 is 1
LCM of denominators i.e. for 420,115 is 9660.
Thus, GCF of Fractions is 1/9660.Finally, GCF of Fractions for 473/420, 653/115 is 1/9660.