Use our free GCF of Fractions Calculator tool to compute the GCF of 704/768, 654/146 i.e 2/56064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 704/768, 654/146.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 704/768,654/146
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 704/768,654/146, numerators are 704,654
Denominators are 768,146
The GCF of 704,654 is 2 .
LCM of 768,146 is 56064.
The greatest common factor of 704/768,654/146 = [GCF of 704,654]/[LCM of 768,146]= 2/56064
Therefore, the GCF of 704/768,654/146 is 2/56064.
To find the highest common factor of 704,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 704,654 is 2.
Lets's calculate GCF of 704,654
2 | 704, 654 |
352, 327 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 704,654 . The biggest common factor number is the GCF number.
So the greatest common factor 704,654 is 2.
Lets's calculate LCM of 768,146
2 | 768, 146 |
384, 73 |
∴ So the LCM of the given numbers is 2 x 384 x 73 = 56064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/56064
Therefore, the GCF of Fractions 704/768,654/146 is 2/56064
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 768,146 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,146) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(768,146) x common factors =2 x 1 = 2
LCM(768,146) = ( 768 × 146 ) / 2
LCM(768,146) = 112128 / 2
LCM(768,146) = 56064
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 704,654?
The HCF of 704,654 is 2
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 704/768, 654/146?
Answer: GCF of Numerators as per given numbers 704/768, 654/146 is
GCF of Numerators i.e. for 704,654 is 2
LCM of denominators i.e. for 768,146 is 56064.
Thus, GCF of Fractions is 2/56064.Finally, GCF of Fractions for 704/768, 654/146 is 2/56064.