Use our free GCF of Fractions Calculator tool to compute the GCF of 286/64, 654/1942 i.e 2/62144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/64, 654/1942.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 286/64,654/1942
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 286/64,654/1942, numerators are 286,654
Denominators are 64,1942
The GCF of 286,654 is 2 .
LCM of 64,1942 is 62144.
The greatest common factor of 286/64,654/1942 = [GCF of 286,654]/[LCM of 64,1942]= 2/62144
Therefore, the GCF of 286/64,654/1942 is 2/62144.
To find the highest common factor of 286,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 286,654 is 2.
Lets's calculate GCF of 286,654
2 | 286, 654 |
143, 327 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 286,654 . The biggest common factor number is the GCF number.
So the greatest common factor 286,654 is 2.
Lets's calculate LCM of 64,1942
2 | 64, 1942 |
32, 971 |
∴ So the LCM of the given numbers is 2 x 32 x 971 = 62144
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/62144
Therefore, the GCF of Fractions 286/64,654/1942 is 2/62144
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 64,1942 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,1942) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(64,1942) x common factors =2 x 1 = 2
LCM(64,1942) = ( 64 × 1942 ) / 2
LCM(64,1942) = 124288 / 2
LCM(64,1942) = 62144
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 286,654?
The HCF of 286,654 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 286/64, 654/1942?
Answer: GCF of Numerators as per given numbers 286/64, 654/1942 is
GCF of Numerators i.e. for 286,654 is 2
LCM of denominators i.e. for 64,1942 is 62144.
Thus, GCF of Fractions is 2/62144.Finally, GCF of Fractions for 286/64, 654/1942 is 2/62144.