Use our free GCF of Fractions Calculator tool to compute the GCF of 493/140, 343/175 i.e 1/700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 493/140, 343/175.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 493/140,343/175
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 493/140,343/175, numerators are 493,343
Denominators are 140,175
The GCF of 493,343 is 1 .
LCM of 140,175 is 700.
The greatest common factor of 493/140,343/175 = [GCF of 493,343]/[LCM of 140,175]= 1/700
Therefore, the GCF of 493/140,343/175 is 1/700.
To find the highest common factor of 493,343, we have to find the factors of both numbers and list the highest common factor.
The factors of 493 are 1, 17, 29, 493
The factors of 343 are 1, 7, 49, 343
The HCF of 493,343 is 1.
Lets's calculate GCF of 493,343
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 493
:1,17,29,493
Now, list down the factors of 343
:1,7,49,343
Greatest Common Factor
We found the factors 493,343 . The biggest common factor number is the GCF number.
So the greatest common factor 493,343 is 1.
Lets's calculate LCM of 140,175
5 | 140, 175 |
7 | 28, 35 |
4, 5 |
∴ So the LCM of the given numbers is 5 x 7 x 4 x 5 = 700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/700
Therefore, the GCF of Fractions 493/140,343/175 is 1/700
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 140,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(140,175) = 35
common factors(in case of two or more numbers have common factors) = 1
GCF(140,175) x common factors =35 x 1 = 35
LCM(140,175) = ( 140 × 175 ) / 35
LCM(140,175) = 24500 / 35
LCM(140,175) = 700
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 493,343?
The HCF of 493,343 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 493/140, 343/175?
Answer: GCF of Numerators as per given numbers 493/140, 343/175 is
GCF of Numerators i.e. for 493,343 is 1
LCM of denominators i.e. for 140,175 is 700.
Thus, GCF of Fractions is 1/700.Finally, GCF of Fractions for 493/140, 343/175 is 1/700.