GCF of 657/342, 318/855
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 657/342, 318/855 i.e 3/1710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 657/342, 318/855.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 657/342,318/855?
Given fractions are 657/342,318/855
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 657/342,318/855, numerators are 657,318
Denominators are 342,855
The GCF of 657,318 is 3 .
LCM of 342,855 is 1710.
The greatest common factor of 657/342,318/855 = [GCF of 657,318]/[LCM of 342,855]= 3/1710
Therefore, the GCF of 657/342,318/855 is 3/1710.
To find the highest common factor of 657,318, 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 318 are 1, 2, 3, 6, 53, 106, 159, 318
The HCF of 657,318 is 3.
Lets's calculate GCF of 657,318
| 3 | 657, 318 |
| 219, 106 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 657,318 By Matching Biggest Common Factor Method
Now, list down the factors of 657
:1,3,9,73,219,657
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
Greatest Common Factor
We found the factors 657,318 . The biggest common factor number is the GCF number.
So the greatest common factor 657,318 is 3.
Lets's calculate LCM of 342,855
| 3 | 342, 855 |
| 3 | 114, 285 |
| 19 | 38, 95 |
| 2, 5 |
∴ So the LCM of the given numbers is 3 x 3 x 19 x 2 x 5 = 1710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1710
Therefore, the GCF of Fractions 657/342,318/855 is 3/1710
Least Common Multiple of 342,855 with GCF Formula
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 342,855 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,855) = 171
common factors(in case of two or more numbers have common factors) = 1
GCF(342,855) x common factors =171 x 1 = 171
LCM(342,855) = ( 342 × 855 ) / 171
LCM(342,855) = 292410 / 171
LCM(342,855) = 1710
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FAQs on GCF of Fractions of 657/342, 318/855
1. What is the HCF of 657,318?
The HCF of 657,318 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 657/342, 318/855?
Answer: GCF of Numerators as per given numbers 657/342, 318/855 is
GCF of Numerators i.e. for 657,318 is 3
LCM of denominators i.e. for 342,855 is 1710.
Thus, GCF of Fractions is 3/1710.Finally, GCF of Fractions for 657/342, 318/855 is 3/1710.