Use our free GCF of Fractions Calculator tool to compute the GCF of 470/346, 140/713 i.e 10/246698 easily. The following is the detailed procedure to determine the greatest common factor of fractions 470/346, 140/713.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 470/346,140/713
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 470/346,140/713, numerators are 470,140
Denominators are 346,713
The GCF of 470,140 is 10 .
LCM of 346,713 is 246698.
The greatest common factor of 470/346,140/713 = [GCF of 470,140]/[LCM of 346,713]= 10/246698
Therefore, the GCF of 470/346,140/713 is 10/246698.
To find the highest common factor of 470,140, we have to find the factors of both numbers and list the highest common factor.
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 470,140 is 10.
Lets's calculate GCF of 470,140
2 | 470, 140 |
5 | 235, 70 |
47, 14 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 470,140 . The biggest common factor number is the GCF number.
So the greatest common factor 470,140 is 10.
Lets's calculate LCM of 346,713
Given numbers has no common factors except 1. So, there LCM is their product i.e 246698
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/246698
Therefore, the GCF of Fractions 470/346,140/713 is 10/246698
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 346,713 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(346,713) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(346,713) x common factors =1 x 1 = 1
LCM(346,713) = ( 346 × 713 ) / 1
LCM(346,713) = 246698 / 1
LCM(346,713) = 246698
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 470,140?
The HCF of 470,140 is 10
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 470/346, 140/713?
Answer: GCF of Numerators as per given numbers 470/346, 140/713 is
GCF of Numerators i.e. for 470,140 is 10
LCM of denominators i.e. for 346,713 is 246698.
Thus, GCF of Fractions is 10/246698.Finally, GCF of Fractions for 470/346, 140/713 is 10/246698.