Use our free GCF of Fractions Calculator tool to compute the GCF of 717/178, 345/274 i.e 3/24386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 717/178, 345/274.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 717/178,345/274
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 717/178,345/274, numerators are 717,345
Denominators are 178,274
The GCF of 717,345 is 3 .
LCM of 178,274 is 24386.
The greatest common factor of 717/178,345/274 = [GCF of 717,345]/[LCM of 178,274]= 3/24386
Therefore, the GCF of 717/178,345/274 is 3/24386.
To find the highest common factor of 717,345, we have to find the factors of both numbers and list the highest common factor.
The factors of 717 are 1, 3, 239, 717
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 717,345 is 3.
Lets's calculate GCF of 717,345
3 | 717, 345 |
239, 115 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 717
:1,3,239,717
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 717,345 . The biggest common factor number is the GCF number.
So the greatest common factor 717,345 is 3.
Lets's calculate LCM of 178,274
2 | 178, 274 |
89, 137 |
∴ So the LCM of the given numbers is 2 x 89 x 137 = 24386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/24386
Therefore, the GCF of Fractions 717/178,345/274 is 3/24386
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 178,274 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(178,274) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(178,274) x common factors =2 x 1 = 2
LCM(178,274) = ( 178 × 274 ) / 2
LCM(178,274) = 48772 / 2
LCM(178,274) = 24386
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 717,345?
The HCF of 717,345 is 3
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 717/178, 345/274?
Answer: GCF of Numerators as per given numbers 717/178, 345/274 is
GCF of Numerators i.e. for 717,345 is 3
LCM of denominators i.e. for 178,274 is 24386.
Thus, GCF of Fractions is 3/24386.Finally, GCF of Fractions for 717/178, 345/274 is 3/24386.