Use our free GCF of Fractions Calculator tool to compute the GCF of 53/312, 35/178, 765/343 i.e 1/9524424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/312, 35/178, 765/343.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 53/312,35/178,765/343
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 53/312,35/178,765/343, numerators are 53,35,765
Denominators are 312,178,343
The GCF of 53,35,765 is 1 .
LCM of 312,178,343 is 9524424.
The greatest common factor of 53/312,35/178,765/343 = [GCF of 53,35,765]/[LCM of 312,178,343]= 1/9524424
Therefore, the GCF of 53/312,35/178,765/343 is 1/9524424.
To find the highest common factor of 53,35,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 53 are 1, 53
The factors of 35 are 1, 5, 7, 35
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 53,35,765 is 1.
Lets's calculate GCF of 53,35,765
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 53
:1,53
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 53,35,765 . The biggest common factor number is the GCF number.
So the greatest common factor 53,35,765 is 1.
Lets's calculate LCM of 312,178,343
2 | 312, 178, 343 |
156, 89, 343 |
∴ So the LCM of the given numbers is 2 x 156 x 89 x 343 = 9524424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9524424
Therefore, the GCF of Fractions 53/312,35/178,765/343 is 1/9524424
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 312,178,343 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,178,343) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(312,178,343) x common factors =1 x 2 = 2
LCM(312,178,343) = ( 312 × 178 × 343 ) / 2
LCM(312,178,343) = 19048848 / 2
LCM(312,178,343) = 9524424
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 53,35,765?
The HCF of 53,35,765 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 53/312, 35/178, 765/343?
Answer: GCF of Numerators as per given numbers 53/312, 35/178, 765/343 is
GCF of Numerators i.e. for 53,35,765 is 1
LCM of denominators i.e. for 312,178,343 is 9524424.
Thus, GCF of Fractions is 1/9524424.Finally, GCF of Fractions for 53/312, 35/178, 765/343 is 1/9524424.