GCF of 318/904, 731/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 318/904, 731/678 i.e 1/2712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 318/904, 731/678.
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 318/904,731/678?
Given fractions are 318/904,731/678
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 318/904,731/678, numerators are 318,731
Denominators are 904,678
The GCF of 318,731 is 1 .
LCM of 904,678 is 2712.
The greatest common factor of 318/904,731/678 = [GCF of 318,731]/[LCM of 904,678]= 1/2712
Therefore, the GCF of 318/904,731/678 is 1/2712.
To find the highest common factor of 318,731, we have to find the factors of both numbers and list the highest common factor.
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The factors of 731 are 1, 17, 43, 731
The HCF of 318,731 is 1.
Lets's calculate GCF of 318,731
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 318,731 By Matching Biggest Common Factor Method
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
Now, list down the factors of 731
:1,17,43,731
Greatest Common Factor
We found the factors 318,731 . The biggest common factor number is the GCF number.
So the greatest common factor 318,731 is 1.
Lets's calculate LCM of 904,678
| 2 | 904, 678 |
| 113 | 452, 339 |
| 4, 3 |
∴ So the LCM of the given numbers is 2 x 113 x 4 x 3 = 2712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2712
Therefore, the GCF of Fractions 318/904,731/678 is 1/2712
Least Common Multiple of 904,678 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 904,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(904,678) = 226
common factors(in case of two or more numbers have common factors) = 1
GCF(904,678) x common factors =226 x 1 = 226
LCM(904,678) = ( 904 × 678 ) / 226
LCM(904,678) = 612912 / 226
LCM(904,678) = 2712
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 318/904, 731/678
1. What is the HCF of 318,731?
The HCF of 318,731 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 318/904, 731/678?
Answer: GCF of Numerators as per given numbers 318/904, 731/678 is
GCF of Numerators i.e. for 318,731 is 1
LCM of denominators i.e. for 904,678 is 2712.
Thus, GCF of Fractions is 1/2712.Finally, GCF of Fractions for 318/904, 731/678 is 1/2712.