Use our free GCF of Fractions Calculator tool to compute the GCF of 657/458, 613/170 i.e 1/38930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 657/458, 613/170.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 657/458,613/170
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 657/458,613/170, numerators are 657,613
Denominators are 458,170
The GCF of 657,613 is 1 .
LCM of 458,170 is 38930.
The greatest common factor of 657/458,613/170 = [GCF of 657,613]/[LCM of 458,170]= 1/38930
Therefore, the GCF of 657/458,613/170 is 1/38930.
To find the highest common factor of 657,613, we have to find the factors of both numbers and list the highest common factor.
The factors of 657 are 1, 3, 9, 73, 219, 657
The factors of 613 are 1, 613
The HCF of 657,613 is 1.
Lets's calculate GCF of 657,613
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 657
:1,3,9,73,219,657
Now, list down the factors of 613
:1,613
Greatest Common Factor
We found the factors 657,613 . The biggest common factor number is the GCF number.
So the greatest common factor 657,613 is 1.
Lets's calculate LCM of 458,170
2 | 458, 170 |
229, 85 |
∴ So the LCM of the given numbers is 2 x 229 x 85 = 38930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38930
Therefore, the GCF of Fractions 657/458,613/170 is 1/38930
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 458,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,170) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(458,170) x common factors =2 x 1 = 2
LCM(458,170) = ( 458 × 170 ) / 2
LCM(458,170) = 77860 / 2
LCM(458,170) = 38930
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 657,613?
The HCF of 657,613 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 657/458, 613/170?
Answer: GCF of Numerators as per given numbers 657/458, 613/170 is
GCF of Numerators i.e. for 657,613 is 1
LCM of denominators i.e. for 458,170 is 38930.
Thus, GCF of Fractions is 1/38930.Finally, GCF of Fractions for 657/458, 613/170 is 1/38930.